Prudent Valuation

Prudent Valuation
Here we go
Global Derivatives Trading & Risk Management
Budapest, 10 May 2016
Marco Bianchetti
Head of Fair Value Policy, Financial and Market Risk Management, Intesa Sanpaolo
Adjunct Professor, University of Bologna
In collaboration with
Umberto Cherubini – Professor of Mathematical Finance, Bologna University
AIFIRM – Association of Italian Financial Risk Managers

M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest, 10 May 2016 p. 2
Summary [1]
1. Introduction
o Overview
o Prudent valuation history
2. Theoretical Background
o Price opacity & financial crisis
o Pricing beyond Black-Scholes
o Market incompleteness & illiquidity
3. Regulation
o Overview
o The Capital Requirement Regulation 575/2013
o The EBA Regulatory Technical Standards
o AVAs vs XVAs
o Prudent valuation reporting
o Prudent valuation data NEW
NEW

Summary [2]
4. AVA calculation
o Definitions and basic assumptions
o Market price uncertainty AVA
o Close-out costs AVA
o Model risk AVA
o Unearned credit spreads AVA
o Investing and funding costs AVA
o Concentrated positions AVA
o Future administrative costs AVA
o Early termination AVA
o Operational risk AVA
5. Prudent valuation framework
o Implementation
o Methodological framework
o Operational framework
o IT framework
o Documentation & reporting
o Example of prudent valuation framework
6. Conclusions
7. References
8. Glossary
NEW

1: Introduction
Overview
Traditionally, quantitative finance practitioners are divided into two populations: those
who seek fair values, i.e. means of price distributions, and those who seek risk
measures, i.e. quantiles of price distributions. Fair value people and risk people typically
live in separate lands, and worship different gods: the profit and loss balance sheet, and
regulatory capital, respectively.
Prudent Valuation is a rather unexplored midland which has recently emerged
somewhere in between the well known mainlands of Pricing and Risk Management. In
fact, the Capital Requirements Regulation (CRR), requires financial institutions to apply
prudent valuation to all fair value positions. The difference between the prudent value
and the fair value, called Additional Valuation Adjustment (AVA), is directly deducted
from the Core Equity Tier 1 (CET1) capital. The Regulatory Technical Standards (RTS)
for prudent valuation proposed by the EBA have been adopted by the EU (reg.
2016/101) on 28th Jan. 2016.
The 90% confidence level required by regulators for prudent valuation links quantiles of
price distributions (exit prices) to capital, thus bridging the gap between the Pricing and
Risk Management mainlands, and forcing the crossbreeding of the fair value and risk
populations above.
In this seminar, we will explore the Prudent Valuation land.

1: Introduction
Overview
Q-Land
Q-measure
Pricing:
extrapolate the
present
Fair value
Profit and loss
P-Land
P-measure
Risk: model the
future
Risk measures
Capital
Prudent Land
Prudent measure
Price distribution
90% exit price
Capital

See A. Meucci, “P versus Q: Differences and Commonalities between the Two Areas of Quantitative Finance”,
GARP Risk Professional, pp. 47-50, February 2011, http://ssrn.com/abstract=1717163
1: Introduction
P vs Q and beyond

The idea of prudent valuation dates back to Basel 2 regulation (see BCBS,
“International Convergence of Capital Measurement and Capital Standards – A revised
framework”, June 2004).
In particular, sec. VI (“Trading book issues”), ch. B (“Prudent valuation guidance”), par.
690-701 set the requirements for prudent valuation in terms of
o systems and controls,
o valuation methodologies,
o valuation adjustments or reserves, impacting regulatory capital (not P&L).
The CRR inherited most of the contents in its art. 105.
In more recent times, prudent valuation has been required by the Financial Stability
Agency (FSA) to UK institutions, see refs. below.
o Financial Services Authority, “Dear CEO Letter: Valuation and Product Control”, August 2008,
http://www.fsa.gov.uk/pubs/ceo/valuation.pdf
o Financial Services Authority, “Product Control Findings and Prudent Valuation Presentation”, November 2010,
http://www.fsa.gov.uk/pubs/other/pcfindings.pdf
o Financial Services Authority, “Regulatory Prudent Valuation Return”, Policy Statement 12/7, April 2012,
http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml
1: Introduction
Prudent valuation history [1/3]

1: Introduction
August 2008
FSA “Dear
CEO letter”
November 2010
FSA “Product Control
Findings and Prudent
Valuation Presentation”
April 2012
FSA “Regulatory Prudent
Valuation Return”, Policy
Statement
2008 2009 2010 2011 20122006 20072004 2005
June 2004
BCBS “International Convergence
of Capital Measurement and
Capital Standards” (Basel 2)

1: Introduction
13 November 2012
EBA Discussion
Paper
(EBA/DP/2012/03)
10 July 2013
EBA Consultation
Paper
(EBA/CP/2013/28)
1 Jan. 2014
CRR
575/2013
31 March 2014
EBA Final Draft RTS
and first application of
prudent valuation
28 Jan. 2016
EBA RTS
published on
OJEU
8 November 2013
EBA Quantitative
Impact Study
2012 2013 2014 2015
23 Jan. 2015
EBA Final Draft
RTS amended
Prudent valuation in
place
2016
28 October 2015
EU commission
adoption of EBA RTS
NEW

Elaborated by AIFIRM Market Risk
Committee, working group on prudent
valuation, 148 pages, publicy available at
http://www.aifirm.it/position-
paper-prudent-valuation
Summary
 Executive summary
 Introduction
 Regulatory requirements
 Prudent Valuation scope
 General assumptions and considerations
 Theoretical background
 AVA calculation under the simplified
approach
 AVA calculation under the core approach
 Prudent valuation operating framework
 Prudent valuation technology
 Conclusions
 Appendixes
 References
 Glossary and notation
1: Introduction
Prudent valuation guidelines and sound practices
NEW

Summary
2. Theoretical background

the crisis, and the Enron case before, has introduced the problem of valuation as a
mean of diffusion of losses among financial institutions and assets.
the problem of getting the price wrong is linked to the fact that, already after the
19th October1987 market crash, the standard Black-Scholes assumptions of
normal distribution of assets returns and perfect replication in continuous time of
all financial products proved wrong.
other sources of risk, not traded in the market, such as volatility and correlation
(smile and skew) have surfaced as key valutation elements. The hedging problem
has become more complex and perfect hedging impossible (the market
incompleteness problem). Moreover, if hedging can be done (volatility swaps or
correlation swaps), it has to be done in highly illiquid markets, or even with OTC
transactions.
o Credit risk: “unearned credit spreads”, that is expected loss due to default of the
counterparty has become the major element in the evaluation of a financial
product. This has added even more focus on hedging complexities.
2: Theoretical background
Introduction

A history of financial crises
 September-October, 1998
LTCM, the major issue of the crisis is the impossibility to replicate financial derivatives
in continuous time, and in perfectly liquid markets. It is the first case of incomplete
markets.
 December, 2001
Enron, the issue is lack of transparency in accounting data. The impact was
uncertainty of valuation of similar companies or companies with the same auditor
(Arthur Andersen). It was called “financial contagion by incomplete information”.
 May 2005
Sudden drop in credit correlation triggered losses in financial intermediaries
absorbing equity risk in securitization deals. It was a case about correlation
uncertainty and hedging risk. Equity hedging strategies based on mezzanine were
turned into losses by a major decrease in correlation.
 2007-2008
Subprime crisis. The crisis themes were illiquidity, lack of transparency and an
increase in correlation (systemic risk). On top of that, the peculiar issue of the crisis
was the role played by the accounting standards in spreading contagion across
intermediaries.

Accounting and the subprime crisis
What is the link between financial crisis and valuation?
 “Default losses on US subprime mortgages about 500 billion dollars.
 But in a mark-to-market world, deadly losses are valuation losses
o Valuation losses as high as 4 trillions.
o Major banks failed without a single penny of default
 BIS study of rescue package: 5 trillions in committed resources. “
Eli Remolona, IV Annual Risk Management Conference, Singapore, July 2010

Toxic assets
.
 “Financial assets the value of which has fallen significantly and may fall
further, especially as the market for them has frozen. This may be due to
hidden risks within the assets becoming visible or due to changes in extremal
market environment”
FT Lexicon
 Toxic assets are a matter of:
o Liquidity (“market frozen”)
o Opacity and ambiguity (“hidden risks becoming visible”)
o “Extremal market environment”

A simple example [1]
 Take a very simple financial product, that is an equity linked note promising to pay a
participation to the increase in some stock market index in five years.
 The replicating portfolio of the product is made up by:
o A zero coupon bond paying the Libor with five years maturity
o A zero coupon bond paying the credit risk spread of the issuer with five years
maturity
o An equity option with five years exercise time
 The main sources of valuation uncertainty are the following.
o The calibration of the five year zero coupon Libor, using fixed income market
data and bootstrapping techniques. This valuation problem is common to other
fixed income products.
o The calibration of the five year zero coupon credit spread, using the issuer’s or
comparable CDS and bond data, and bootstrapping techniques.
o The calibration of the five year equity volatility, using equity options’ market data
and bootstrapping techniques. Typically, exchange traded or OTC derivatives do
not have a liquid market for 5 years maturity and we must extend implied
volatility beyond the traded maturities.

A simple example [2]
 There are actually other risk sources, mostly the correlations among the risk factors
involved.
o Correlation between equity and bonds
It could seem that this should not affect the pricing problem, since it is made under
the Forward Martingale Measure (FMM), but the volatility of the forward price
depends on correlation.
o Correlation between underlying asset and volatility
This is relevant in cases in which the underlying asset and its volatility co-move in
directions leading to a decrease of the embedded option. This is not the case of
this product, which is long both in the underlying asset and its volatility, while the
equity market and volatility are known to be negatively correlated.
o Correlation between the embedded option and the credit quality of the issuer
Actually the embedded option is a vulnerable option whose value is affected by the
positive correlation between the exposure (the exercise of the option) and the
default probability of the issuer.

Incomplete markets: definition
 Complete markets are defined by all financial products being “attainable”. This means
that the payoff of every financial contract or product can be exactly replicated by some
trading strategy. This implies lack of frictions and continuous rebalancing of the
replicating portfolio. Markets are assumed to be perfectly liquid and trading is
costless.
 If markets are complete, there exists a unique Equivalent Martingale Measure (EMM)
such that the price of each and every asset can be computed by the expected value
under such measure, and discounted with the risk-free rate. With complete markets
the price of each financial product would be unique, and there would be no valuation
uncertainty problem.
 Real world markets are incomplete and there exists a valuation uncertainty problem.
The reason is that no perfect hedge exists. More precisely, the reasons for incomplete
markets are:
o there are not enough assets to hedge all possible risk factors (no enough Arrow-
Debreu prices);
o replicating portfolios cannot be rebalanced in continuous time in such a way as to
allow for a perfect hedge;
o there is not enough liquidity in the market, particularly in stress times, to allow
rebalancing of the replicating portfolios.

Incomplete markets: theory
 From a technical point of view, selecting a price in incomplete markets amounts to
choose a probability measure (pricing kernel) in a set of probability measures. This set
 contains the probabilities such that the price of each product is a martingale. This
implies that for each product it is not possible to find a replicating strategy that attains
the product for sure.
𝑉𝑄 𝑡 = 𝔼 𝑄 𝐷(𝑡, 𝑇)𝑉(𝑇)ȁ 𝑄 ∈ ℘
 The problem is then to define:
 the set of probabilities  including all the risk-neutral probabilities;
 a strategy to select a probability in the set.
 Notice that the problem of selecting a probability amounts to selecting a lottery. So, a
possible strategy to select a specific probability is to use expected utility or some of its
extensions.
 Hedging error: every probability measure that is chosen is subjected to hedging error.
Based on this, for example, one could select the probability with the lowest hedging
variance, in the set with some expected hedging cost.

Incomplete markets: back to expected utility
 We remind that expected utility ranks lotteries by the expected value of a function of
the pay-off. The function weighting the pay-off is increasing and concave (for risk-
averse decision makers) and is called utility function. So, lottery A is preferred to
lottery B if
E(U(A)) > E(U(B))
with U(x) the utility function.
 Ellsberg paradox: what happens if the probability of some lottery is not known for
sure? If there is a preference for the lottery whose probability is known, or for the
other, the expected utility does not work.
 Example: there are 90 balls in an urn, we know that 30 are Red, and the others are
Blue or Green. Do you have any preference between:
 A lottery paying a premium if the ball is Red
 A lottery paying a premium if the ball is Blue
 Now consider the choice between:
 A lottery paying a premium if the ball is Blue or Green
 A lottery paying a premium if the ball is Red or Green
 If you have preferences of Red over Blue, then Prob(Red) = 1/3 > Prob(Blue), by
consistently: Prob(Red  Green) < Prob(Blue  Green) = 2/3 and Prob(Blue) > 1/3

Incomplete markets: non-additive expected utility
 Notice that the problem with expected utility is additivity. In fact, since additivity means
Prob(A  B) = P(A) + P(B), for A and B disjoint, we have
Probl(Red) + Prob (Green) > Prob(Blue) + Prob(Green)
which implies Prob(Red) > Prob(Blue).
 This implies that allowing for the preferences in the two lotteries to be represented by
the same measure one has to break down additivity.
 Non additive representations of preferences are called capacities. These measures
are monotone and are not required to be additive. The expected value with respect to
capacities is represented by the Choquet integral.
 There is a duality relationship between sub and super additive capacities and
between lower and upper Choquet integrals. The duality reminds of the Dempster-
Shafer theory.
 We will see that this representation is important to represent the set of probability
measures.

Alternative theories for price bounds
 There are two different approaches to address valuation uncertainty. In both cases the
price bounds are obtained by assuming interval valuation.
 Uncertain Volatility Model
 Volatility is assumed be included in a given interval
 This leads to two conservative pricing bounds (BSB PDE functions)
 Avellaneda, Levy and Paràs (1996), AMF
 Choquet pricing
 Interval probabilities (MMEU, Gilboa and Schmeidler, 1989)
 Conservative valuation (Choquet integral)
 Cherubini (1997) AMF, Cherubini and Della Lunga (2001) AMF
AMF = Applied Mathematical Finance
 MMEU: assume the worst possible probability scenario and select the choice that
yields the maximum expected utility.

Uncertain Volatility Model
 Set the delta-neutral portfolio
 Volatility choice
 The Black-Scholes formula becomes non linear (Black-Scholes-Baremblatt)
where
arg min
𝜎 𝑚𝑖𝑛≤𝜎≤𝜎 𝑚𝑎𝑥
1
2
𝜎2 𝑆2
𝜕2
𝑔
𝜕𝑆2
=
𝜎 𝑚𝑖𝑛, 𝑖𝑓
𝜕2 𝑔
𝜕𝑆2 > 0,
𝜎 𝑚𝑎𝑥, 𝑖𝑓
𝜕2
𝑔
𝜕𝑆2
< 0.
min
𝜎 𝑚𝑖𝑛≤𝜎≤𝜎 𝑚𝑎𝑥
𝑑Π =
𝜕𝑔
𝜕𝑡
+
1
2
𝜎2
𝑆2
𝜕2
𝑔
𝜕𝑆2 𝑑𝑡 = 𝑟Π = 𝑟 𝑔 − 𝑆
𝜕𝑔
𝜕𝑆
.
𝜎2
𝜕2
𝑔
𝜕𝑆2
+
: =
𝜎 𝑚𝑖𝑛
2
, 𝑖𝑓
𝜕2
𝑔
𝜕𝑆2
> 0,
𝜎 𝑚𝑎𝑥
2
, 𝑖𝑓
𝜕2
𝑔
𝜕𝑆2 < 0.
𝜕𝑔
𝜕𝑡
+
1
2
𝜎2 𝜕2 𝑔
𝜕𝑆2
+
𝑆2 𝜕2 𝑔
𝜕𝑆2 + 𝑟𝑆
𝜕𝑔
𝜕𝑆
− 𝑟𝑔 = 0,

Choquet pricing
 Long and short positions
 Long and short positions are represented by Choquet integrals with respect to
capacities.
 Given a function f and a non-additive measure 𝑄𝑠𝑢𝑏, the upper and lower Choquet
integrals are defined as
𝑉𝑄 𝑡 =
min
𝑄∈℘
න𝐷 𝑡, 𝑇 𝑔 𝑆, 𝑇 𝑑𝑄 , long position,
max
𝑄∈℘
න𝐷 𝑡, 𝑇 𝑔 𝑆, 𝑇 𝑑𝑄 , short position.
න
−∞
0
𝑄𝑠𝑢𝑏 𝑓 ≤ 𝑥 𝑑𝑥 + න
0
+∞
1 − 𝑄𝑠𝑢𝑏 𝑓 ≤ 𝑥 𝑑𝑥 , lower Choquet integral,
න
−∞
0
1 − 𝑄𝑠𝑢𝑏 𝑓 ≥ 𝑥 𝑑𝑥 + න
0
+∞
𝑄𝑠𝑢𝑏 𝑓 ≥ 𝑥 𝑑𝑥 upper Choquet integral.

Choquet pricing
 Assume the Breeden and Litzenberger representation of the pricing kernel and the
corresponding call and put prices. According to Breeden and Litzenberger the
probability of exercise of an option can be recovered from the derivative of the option
with respect to the strike price.
 By integrating the pricing kernel we can then recover the prices of call and put options
as a function of the integral of cumulative distributions, that is, as Choquet integrals,
−
1
𝑃 𝑡, 𝑇
𝜕𝐶𝑎𝑙𝑙
𝜕𝐾
= 𝑄 𝑆 𝑇 > 𝐾 , ⇒ 𝐶𝑎𝑙𝑙 𝑡 = 𝑃(𝑡, 𝑇) න
𝐾
+∞
)1 − 𝑄(𝑥 𝑑𝑥 ,
1
𝑃 𝑡, 𝑇
𝜕𝑃𝑢𝑡
𝜕𝐾
= 𝑄 𝑆 𝑇 ≤ 𝐾 ⇒ 𝑃𝑢𝑡 𝑡 = 𝑃(𝑡, 𝑇) න
−∞
𝐾
𝑄(𝑥)𝑑𝑥 .

Examples of valuation uncertainty
 Derivatives with counterparty risk
CVA and DVA with correlation between the underlying asset and the credit risk of the
counterparty (wrong way risk)
 Toxic assets
Example: a senior tranche, with high attachment, of a securitization deal traded on the
market at much lower value.
 Correlation products
that is Breeden and Litzenberger representation of the pricing kernel and the
corresponding call and put prices. Example: options on baskets.
 Illiquid derivatives with concentration risk
Large derivative positions require large positions of the underlying asset for delta
hedging. Example: large plain vanilla calls/puts on funds.

CVA valuation
 Assume that the payment schedule of a swap be {t1, t2,…, tn} and that default of the
counterparty receiving fixed rate (B) occurred between tj-1 and tj. In this case the loss
suffered by the surviving counterparty A will be
where sr is the swap rate at the date of default and k is that at the origin.
 By the same token, the loss suffered by B due to default of A will be
    
 
1-n
ji
1A 0,,max,Lgd nji ttsrkttP
    
 
1-n
ji
1B 0,,max,Lgd kttsrttP nji

CVA valuation with copula function
 Denote GB(tj) the survival probability of party B beyond time tj. Then, the default
probability between time tj - 1 and time tj is GB(tj-1) – GB(tj). Moreover, assume C(u,v)
to be a copula function, and Q(x) the pricing kernel of the swap rate
 Then the CVA for counterparty A will be
         



 
1
11 ,1,
n
ji K
jBjBiB dtGtGQCttPLgd 

CVA valuation with wrong way risk
 Now assume perfect dependence between the underlying asset and default of the
counterparty. In this case, we have the Fréchet bound 𝒞 𝑥, 𝑦 ≤ 𝑀𝑖𝑛 𝑥; 𝑦 .
In this case, the CVA can be computed in closed form as
CVA = LgdBmax[k*(tj) – k,0]A(t, tj, tn) [GB(tj-1) – GB(tj)]
– LgdB PayerSwaption(.;max(k*(tj),k))
where k*(tj) is defined from Q((sr(tj,tn) > k*(tj)) = GB(tj-1) – GB(tj), and
is the swap annuity.
𝐴(𝑡; 𝑡𝑗, 𝑡 𝑛) = ෍
𝑖=𝑗
𝑛−1
𝑃 𝑡, 𝑡𝑖−1 𝜏𝑖

CVA valuation with wrong way risk
o For the short end of the contract the worst scenario is perfect negative dependence
between the underlying asset and default of the counter party. In this case, we have
the Fréchet bound 𝒞 𝑥, 𝑦 > 𝑀𝑖𝑛 𝑥 + 𝑦 − 1; 0 .
In this case, the CVA can be computed in closed form as
CVA = LgdA[ReceiverSwaption(.;min(k*(tj),k)) – Receiver swaption(.;k)]
+ LGDA max[k – k*(tj),0](1 – GA(tj – 1) – GA(tj))

CVA valuation with wrong way risk (long party)
Vulnerable Call Swaptions: Financial Institution Paying Fixed
0
0,002
0,004
0,006
0,008
0,01
0,012
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Independence
Perfect positive dependence

CVA valuation with wrong way risk (short party)
Vulnerable Put Swaptions: Financial Institution Receiving Fixed
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
0,004
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Independence
Perfect Negative Dependence

Tranche senior
 Assume a senior tranche with attachment equal to 30%, so that it begins to absorb
losses only from 30% of collateral on.
 Assume a standard valuation model such as Vasicek asymptotic model, that is based
on the assumption that all exposures in the basket have the same default probability
P and the same asset correlation  with systemic risk.
 Then, the expected loss of a senior tranche with attachment 𝐿 𝑑 is
𝐸𝐿 = 𝑃 − 𝑁 𝑁−1 𝑃 , 𝑁−1 𝐿 𝑑 , 1 − 𝜌2
where 𝑁 𝑁−1
𝑥 , 𝑁−1
𝑦 , 𝜌 is the Gaussian copula function.
 Now notice that by considering the two extreme values of the copula function
𝒞 𝑥, 𝑦 = 𝑥𝑦 and 𝒞 𝑥, 𝑦 = min(𝑥, 𝑦) yields extreme values for the expected losses of
the senior tranche.

Tranche senior: pricing bounds
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Rho = 0
Rho = 1

Rainbow options
 Assume a call option on the minimum of a set of assets (Everest). This can be priced
with a Choquet integral using the copula as the Choquet integral
 From the point of view of the issuer, we can compute the conservative value in closed
form, for a bivariate product
     dTSQTSQTSQCTtP
TKSSSCall
K
N
N




))((),...)((),)((,
),),,...,(min(
21
21
       
    
 )*,max(;,
;,*;,
,,
2
11*
*],max[
2
*
11* 2
KKtSC
KtSCKtSC
dSQTtPdSQTtPC
KK
KK
K
K
KK





 
1
1 

Dynamic replication of illiquid derivatives
 Now assume you are trading a derivative with a costumer, maybe for a large quantity
of the underlying asset (concentration risk) or for an illiquid underlying. In this case,
standard textbook references for the pricing of options do not apply, since the
production process of the derivative has an impact on the underlying asset.
 Here the only process is to start with a dynamics of the underlying asset and to try a
replication strategy, allowing for the liquidity cost of rebalancing the portfolio, and the
funding cost of changing the leverage position. So, the market price incorporates
liquidity costs, both in the sens of market liquidity and funding liquidity. Both the
sources of cost are all the more relevant the larger the size of the position.
 The problem of finding an optimal trade-off between liquidity cost and liquidity risk is
extremely involved. In fact, it requires to define trading strategies: how many times to
rebalance, when, whether at fixed intervals or contingent on some rule.
 The problem is magnified by the need to specify the market impact function, that
includes:
 Which is the trade off between the market impact due to sudden rebalance
trades versus the volatility risk to which one is exposed for partitioned unwinding
 How much of the market impact is temporary and how much is permanent.
Permanent impacts make the problem particularly involved.

Summary
3. Regulation
o Overview
o The Capital Requirement Regulation 575/2013
o The EBA Regulatory Technical Standards
o AVAs vs XVAs
o Prudent valuation reporting
o Prudent valuation data

3: Regulation
Overview
 Articles 34 and 105 of Capital Requirements Regulation (CRR, n. 575/2013), in force
since 1 January 2014, require financial institutions to apply prudent valuation to all fair
value positions (included positions outside the trading book), setting a new prudential
requisite for regulatory capital including valuation uncertainty.
 The difference between the prudent value and the fair value, accounted in the
institution’s balance sheet, is called “Additional Valuation Adjustment” (AVA), and is
directly deducted from the Core Equity Tier 1 (CET1) capital.
 Following the CRR, the EBA published a Discussion Paper (EBA/DP/2012/03), a
Consultation Paper (EBA/CP/2013/28), and a Final Draft (EBA/RTS/2014/06), to be
approved by the EU Commission, setting the Regulatory Technical Standards (RTS)
for prudent valuation.
 The EBA Final Draft defines the AVA calculation methodology using two alternative
approaches, named Simplified Approach and Core Approach. The Final Draft sets
also the requirements on systems, controls and documentation that should support
the prudent valuation process.
 Acronyms: CRR, AVA, CET1, EBA, RTS, EU,
 Keywords: fair/prudent value, simplified/core approach

Market
Data
Models
Estim
ates
Fair Value
accounting AVA
(Additional
Valuation
Adjustment)
IFRS 13
Prudent valuation
Prudent value
Deducted from Common
Equity Tier 1 capital
CRR article 105 requisites
Policies &
procedures
Control
systems
Prudent
valuation
principles
3: Regulation
CRR 575/2013 [1/8]

3: Regulation
CRR 575/2013 [2/8]
Art. 34
Prudent valuation
scope
Systems and
controls
Valuation
Valuation
adjustments
Art. 105
CRR
575/2013
CRR Prudent Valuation Tree
Prudent valuation
principles
Degree of certainty, art. 105.1
S&C requirements, art. 105.2
Revaluation frequency art. 105.3
Mark to market, art. 105.4-5
Mark to model, art. 105.6-7
IPV, art. 105.8
Valuation adjustments, art. 105.9-10
Illiquid positions, art. 105.11
Other valuation adj., art. 105.12
Complex products, art. 105.13

 CRR art. 34: scope and target
o Scope: all assets measured at fair value
o Target: CET1 capital (not P&L)
3: Regulation
CRR 575/2013 [3/8]

 CRR art. 105.1, scope and degree of certainty: all positions are subject to prudent
valuation, achieving an appropriate degree of certainty with regard to:
o the dynamic nature of the positions,
o the demands of prudential soundness, and
o the mode of operation and purpose of capital requirements in respect of trading book
positions.
 CRR art 105.2, systems and controls: institutions establish and maintain systems and
controls to ensure prudent and reliable valuations, including at least.
o Documented policies and procedures for the valuation process, including:
• clearly defined responsibilities of the various areas involved in the determination of the
valuation,
• sources of market information and review of their reliability,
• guidelines for the use of unobservable inputs that reflect the assumptions of authority on
the elements used by market participants to determine the price of the position,
• frequency of independent valuation,
• timing of closing prices,
• procedures for the correction of assessments,
• procedures for the reconciliation of month end and ad hoc.
o Clear and independent (of the front office) reporting lines for the department in charge of the
valuation process.
3: Regulation
CRR 575/2013 [4/8]

 CRR art 105.3, revaluation frequency: institutions revalue trading book positions at
least daily
 CRR art 105.4-5, mark to market: institutions mark their positions to market whenever
possible, using the more prudent side of bid and offer unless they can close out at mid
market.
 CRR art 105.6, mark to model: where marking to market is not possible, institutions
must conservatively mark to model their positions and portfolios.
3: Regulation
CRR 575/2013 [5/8]

 CRR art 105.7, mark to model:
o senior management must be aware of the fair-valued positions marked to model and must
understand the materiality of the uncertainty of the risk/performance of the business;
o source market inputs, where possible, in line with market prices, and assess the
appropriateness of market inputs and model parameters on a frequent basis;
o use valuation methodologies which are accepted market practice;
o where the model is developed by the institution itself, it must be based on appropriate
assumptions, assessed and challenged by suitably qualified parties independent of the
development process;
o have in place formal change control procedures, hold a secure copy of the model and use
it periodically to check valuations;
o risk management must be aware of the weaknesses of the models used and how best to
reflect those in the valuation output;
o models are subject to periodic review to determine the accuracy of their performance,
including assessment of the continued appropriateness of assumptions, analysis of profit
and loss versus risk factors, and comparison of actual close out values to model outputs;
o the model must be developed or approved independently
of the trading desk and independently tested, including
validation of the mathematics, assumptions and software
implementation.
3: Regulation
CRR 575/2013 [6/8]
Very detailed article
regarding valuation
in general

 CRR art. 105.8, independent price verification (IPV): institutions perform independent
price verification in addition to daily marking to market/model. Verification of market
prices and model inputs must be performed by unit independent from units that benefit
from the trading book, at least monthly, or more frequently depending on the nature of
the market or trading activity. Where independent pricing sources are not available or
pricing sources are more subjective, prudent measures such as valuation adjustments
may be appropriate.
 CRR art 105.9-10: valuation adjustments: institutions establish and maintain
procedures for considering valuation adjustments, and formally consider the following:
unearned credit spreads, close-out costs, operational risks, market price uncertainty,
early termination, investing and funding costs, future administrative costs and, where
relevant, model risk.
 CRR art 105.11, illiquid/concentrated positions: Institutions shall establish and
maintain procedures for calculating an adjustment to the current valuation of any less
liquid positions, which can in particular arise from market events or institution-related
situations such as concentrated positions and/or positions for which the originally
intended holding period has been exceeded.
3: Regulation
CRR 575/2013 [7/8]

 CRR art. 105.12, other valuation adjustments:
institutions must consider whether to apply a valuation adjustment also:
o when using third party valuations,
o when marking to model,
o for less liquid positions, including an ongoing basis review their continued suitability,
o for uncertainty of parameter inputs used by models.
 CRR art. 105.13, complex products: institutions must explicitly assess the need for
valuation adjustments to reflect the model risk associated with using:
o a possibly incorrect valuation methodology
o unobservable (and possibly incorrect) calibration parameters in the valuation model.
3: Regulation
CRR 575/2013 [8/8]

3: Regulation
Fair Value Vs Prudent Value [1]
Fair Value
o Regulation: IFRS13
o Application: balance sheet
o Percentile: 50% (expected
value)
o The price that would be received
to sell an asset or paid to
transfer a liability in an orderly
transaction between market
participants at the measurement
date
o Must include all the factors that
a market participants would use,
acting in their economic best
interest.
o Atoms: single trades.
o Fair value adjustments
o Non-entity specific
Prudent value
o Regulation: CRR/EBA
o Application: CET1
o Percentile: 90%
o Must reflect the exit price at which
the institution can trade within the
capital calculation time horizon.
o Atoms: valuation positions subject
to a specific source of price
unertainty
o Entity specific
o Subject to diversification benefit
(50% weight for MPU, CoCo, MoRi
AVAs)

3: Regulation
Fair Value Vs Prudent Value [2]
Why capital and not P&L ?
 P&L is accounted under accounting standards
o EU listed companies: use IFRS (International Financial Reporting Standards),
established and maintained by the IASB (International Accounting Standards
Board) see www.ifrs.org
o US listed companies: use GAAP (Generally Accepted Accounting Standards),
established and maintained by the FASB (Financial Accounting Standards Board),
see www.fasb.org
o Convergence towards IFRS is in progress
 Both IFRS and GAAP define the fair value as an exit price, not as a prudent price. Fair
value must be fair, not prudent.
 Thus, regulators have decided to account for prudent price through capital, instead of
altering the accounting standards.

3: Regulation
Overlaps and possible offsets
AVAs have to be deducted by CET1. Hence, possible double counting w.r.t. other capital
deductions should be considered.
 AVA UCS vs Expected Loss Amounts
CRR article 159 states that “Institutions shall subtract the expected loss amounts
calculated in accordance with Article 158 (5), (6) and (10) from the general and specific
credit risk adjustments and additional value adjustments in accordance with Articles 34
and 110 and other own funds reductions related to these exposures…”.
The Credit Risk capital requirements, including the expected loss (EL) amount, are
calculated using the higher accounting values, not the AVA adjusted values. As a result,
without an adjustment to the capital requirements on those assets, there is a double hit
to capital. The AVA UCS offset against EL, in Article 159, is a mitigation that prevents
from double hit.
 Day One Profit & Loss deductions
Since these are deductions from profit and loss to account for fair value uncertainty, it
seems that there exist a double counting with AVAs, and AVAs can be reduced
accordingly. See survey.
 Others
To be understood and clarified, possibly with regulators.

3: Regulation
EBA RTS: overview
 The EBA RTS issued on 23rd Jan. 2015 have been adopted by the EU with Commission
delegated regulation (EU) 2016/101, published on the OJEU on
 The RTS set the detailed regulatory technical standards on prudent valuation under
articles 34 and 105 of CRR
 The most important feature of the EBA RTS is the distinction between two different
approaches for the implementation of the prudent valuation methodology: the simplified
approach and the core approach.
 The choice between the two approaches depends on a threshold on the sum of the
absolute values of fair-valued assets and liabilities. The EBA sets the threshold at EUR
15 billion.
 The EBA RTS sets further requirements in terms of documentation (art. 18), systems
and controls (art. 19). These provisions essentially require Institutions to have in place a
two-level internal policy for fair value (Fair Value Policy) and for prudent value (Prudent
Valuation Policy).

3: Regulation
EBA RTS: overview
General
provisions
Sec. 1
Core
approach
Sec.3
EBA RTS
Final draft
EBA RTS Prudent Valuation Tree
Simplified
approach
Sec.2
Documentation
systems &
controls
Sec.4
Methodology for AVA, art. 1
Definitions, art. 2
Sources of market data, art. 3
Conditions of application, art. 4
AVA calculation, art. 5
AVA aggregation, art. 6
Overview, fall back, art. 7
General provisions, art. 8
AVA calculation, art. 9-17
Documentation, art. 18
Systems & controls, art. 19
Entry into force, art. 20 AVA OpR, art. 17
AVA EaT, art. 16
AVA FAC, art. 15
AVA CoPo, art. 14
AVA IFC, art. 13
AVA UCS, art. 12
AVA MoRi, art. 11
AVA CoCo, art. 10
AVA MPU, art. 9

3: Regulation
EBA RTS: prudent valuation scope [1/9]
General rules
 Region of application: since the CRR is an EU directive, prudent valuation applies to
all institutions within EU countries. In case of institution made of a central holding and
one or more subsidiaries, prudent valuation applies to those individual subsidiaries
included in EU countries.
 Scope of application: the CRR art. 5, defines the prudent valuation scope as including
all trading book positions. However, the CRR art. 34 requires that institutions apply the
standards of art. 105 to all assets measured at fair value. The combination of the above
CRR articles 34 and 105 implies that the prudent valuation scope includes all fair-valued
positions, regardless of whether they are held in the trading book or banking book.
The positions at fair value held in both trading and banking books are the following:
Assets Liabilities
Financial assets held for trading (HFT) Financial liabilities held for trading (HFT)
Financial assets at fair value Financial liabilities at fair value
Financial assets available for sale (AFS) (for
the portion not subject to prudential filters)

3: Regulation
 Positions excluded:
o the EBA RTS, art. 4.2 and 8.1, allow Institutions to exclude partially or totally from the
prudent valuation scope those positions for which a change in their accounting fair
value has only a partial or zero impact on Common Equity Tier 1 capital. These
positions must be included in proportion to the impact of the relevant valuation
change on CET1 capital.
o In particular these positions are the following:
1. positions subject to prudential filters,
2. exactly matching, offsetting positions (back to back),
3. positions in hedge accounting.
o Notice that, since the size of the positions above may be relevant, the prudent
valuation scope is the primary driver of the AVA figures.
o How to compute inclusion/exclusion in practice ? See next slides.

3: Regulation
1. Positions subject to prudential filers
o Positions subject to prudential filters refer to the "Financial assets available for sale"
(AFS). The inclusion/exclusion of these positions from the prudent valuation scope
of application follows the CRR requirements.
o The exact percentages of partial inclusions follows the transitional provisions that
each local Regulator issued in compliance with the above CRR requirements.
o Partial inclusion means, for instance, that if 40% of fair value gains and losses are
filtered in CET1, the residual 60% of fair value gains and losses are included in the
prudent valuation scope. In case of 100% filter, the position is completely excluded
by prudent valuation.
Position under prudential filters (AFS) Inclusion
Government bonds issued by EU countries 0%
Other debt securities (excluding the EU
government bonds above)
Partial inclusion depending on the sign of
the reserve and on local prescriptions
Equity
Partial inclusion depending on the sign of
the reserve and on local prescriptions

Transitional provisions issued by national regulators.
3: Regulation
Circolare 285 Banca d’Italia
The applicable percentage following art. 467, par. 3 CRR is:
a) 20% since 1 Jan. 2014 to 31 Dec. 2014
b) 40% since 1 Jan. 2015 to 31 Dec. 2015
c) 60% since 1 Jan. 2016 to 31 Dec. 2016
d) 80% since 1 Jan. 2017 to 31 Dec. 2017
Local
regulation
in Italy
Article 467 CRR
[…] institutions shall include in the calculation of their Common
Equity Tier 1 items only the applicable percentage

3: Regulation
Institutions may not include in own funds unrealized gains and losses related to AFS
positions with central administrations.
Circolare 285 Banca d’Italia
The applicable percentage following art. 468, par. 3 CRR is:
a) 100% 1 Jan. 2014 to 31 Dec. 2014
b) 60% since 1 Jan. 2015 to 31 Dec. 2015
c) 40% since 1 Jan. 2016 to 31 Dec. 2016
d) 20% since 1 Jan. 2017 to 31 Dec. 2017
Article 468 CRR
[…] institutions shall remove in the calculation of their Common
Equity Tier 1 items only the applicable percentage
Local
regulation
in Italy

3: Regulation
According to Regulation (EU) 2016/445 of the European Central Bank of 14 Mar 2016
(published OJEU on 26 Mar. 2016), art. 14 and 15, the corresponding art. 467 and 468
of CRR (setting prudential filters for AFS positions) are modified such that AFS positions
in EU government Bonds shall no longer subject to 100% filter, but shall be subject to
standard prudential filters holding for other AFS position:
 Inclusion of unrealized losses (art. 14 -> art. 467 CRR):
o 60% in [1/1/2016 – 31/12/2016]
o 80% in [1/1/2017 – 31/12/2017]
 Exclusion of unrealized gains (art. 15 -> art. 468 CRR):
o 40% in [1/1/2016 – 31/12/2016]
o 20% in [1/1/2017 – 31/12/2017]
 First application date: Q4-2016
This regulatory change will change substantially the AVA figures for institutions
with huge positions in EU govies (more or less all banks...).
NEW

3: Regulation
2. Exactly matching, offsetting positions (back to back)
o Back to back positions are groups of trades with total null valuation exposure to
market risk factors (interest rates, volatility, etc.), since any variation in the relevant
market valuation inputs generates opposite variations in the value of the trades in
the group, such that the total value is constant. In other words, the group has null
total sensitivity to market risk factors.
o We stress that back to back positions are neutral w.r.t. other risk factors, such as
counterparty defaults, since the trades into the group may be subscribed with
different counterparties.
o From a prudent valuation point of view:
• Simplified approach: 100% exclusion (EBA RTS art. 4.2)
• Core approach: AVAs must be calculated based on the proportion of the
accounting valuation change that impacts CET1 capital (EBA RTS art. 8.1). In
practice:
• AVA MPU, CoCo and MoRi are null,
• AVA UCS, IFC, CoPo, FAC, EaT, OpR must be computed on the total
valuation exposure of the back to back portfolio.

3: Regulation
3. Hedge accounting positions
o Hedge accounting positions are characterized by a hedged instrument (e.g. one ore
more securities, loans or mortgages, etc.) and an hedging instrument (e.g. one ore
more interest rate swaps, credit default swaps, etc.).
o The total package of hedged + hedging instruments has, by construction, a reduced
sensitivity to the underlying risk factors.
o From a prudent valuation point of view, all AVAs must be computed on the total
valuation exposure of the hedge accounting portfolio.

3: Regulation
Positions subject
to prudential
filters (AFS)
Positions in
hedge
accounting
Positions for which a
change in their
accounting fair value
has only a partial or
zero impact on CET 1
Art. 4.2 and 8.1
EBA RTS Prudent Valuation scope: exclusions
Positions in
back to back
EU Gov. bonds
Other bonds
Equity
General criteria
for exclusion
Positions excluded
% of
exclusion
100% until Sept. 16
Partial, phase in
Partial, phase in
Simplified appr.
Partial, residual exposure
of hedged + hedging items
Core appr.
100%
Partial, residual exposure
to UCS, IFC, CoPo, FAC,
EaT, OpR AVAs

3: Regulation
EBA RTS: simplified approach
Simplified Approach
(EBA RTS, sec. 2)
 Institutions may apply the Simplified Approach if the sum of the absolute value of
fair-valued assets and liabilities is less than EUR15 bn.
 The Simplified Approach AVA is given by the 0,1% of the sum of the absolute value
of fair-valued assets and liabilities.
Example of AVA calculation under the simplified approach. Data do not refer to real portfolios.
Below
threshold

3: Regulation
EBA RTS: core approach [1/3]
Core Approach (EBA RTS, sec. 3)
 Institutions that at individual or consolidated level exceed the EUR15bn threshold must
apply the core approach.
 Each AVA is the excess of valuation adjustments required to achieve the identified
prudent value, over any adjustment applied in the institution’s fair value that can be
identified as addressing the same source of valuation uncertainty as the AVA.
 Whenever possible, the prudent value of a position is linked to the 90% percentile of its
price distribution. In practice for AVAs i) Market price uncertainty ii) Close-out costs iii)
Unearned credit spreads, the Institutions must compute the prudent value using the
available market data and the 90% target confidence.
 Whenever insufficient data exists to construct a plausible range of values, institutions
shall use an expert-based approach using qualitative and quantitative information
available to achieve a 90% level of certainty in the prudent value.
Additional Valuation
Adjustments

3: Regulation
Core approach
Additional Valuation Adjustments
Market
Price
Uncertainty
(MPU)
Art. 9
Close Out
Costs
(CoCo)
Art. 10
Model Risk
(MoRi)
Art. 11
Unearned
Credit
Spread
(UCS)
Art. 12
Investing &
Funding
Cost
(IFC)
Art. 13
Concen-
trated
Positions
(CoPo)
Art. 14
Future
Admin
Costs
(FAC)
Art. 15
Early
Termination
(EaT)
Art. 16
Main
AVAs
UCS/IFC
AVAs
Other
AVAs
Operational
Risk
(OpR)
Art. 17
The AVA hierarchy
Market risk factors
50% weights for diversification
Market risk factors
Split onto main AVAs
Non-market risk factors
100% weights, no diversification

3: Regulation
Example of AVA calculation and aggregation
under the core approach.
IFC and UCS AVAs are split into their MPU, CoCo and
MoRi components and pre-aggregated to the
corresponding AVAs, then the total AVA is obtained from
the aggregation of the other seven residual AVAs. In order
to show toy but realistic figures, we assumed the principal
AVAs equal to 1/7 of the 99% x 0.1% of the total FV under
the core approach. AVA OpR has been calculated as for a
non-AMA Institution. In the last line, we also add a
possible AVA fall-back calculated on the remaining 1% x
0.1% of the total FV.
Above
threshold

3: Regulation
EBA RTS: fall-back approach [1/2]
Fall back approach (EBA RTS, art. 7.2.b)
Institutions that exceed the EUR15bn threshold but cannot calculate the core approach
AVAs for certain positions, are allowed to apply a «fall-back approach» (actualy very
capital intensive), and compute AVAs for those positions as the sum of:
 100% of the net unrealised profit (NUP)
 10% of the notional value in case of derivatives;
 25% of the absolute difference between the fair value (FV) and the net unrealised
profit for non-derivatives.
In formulas:
"unrealised profit shall mean the change, where positive, in fair value since trade
inception, determined on a first-in-first-out basis.”
A𝑉𝐴 𝑓𝑏 = 100% 𝑁𝑈𝑃+
+ 10% 𝑁 𝐷𝑒𝑟 + 25% 𝐹𝑉 − 𝑁𝑈𝑃+
𝑁𝑜𝑛−𝐷𝑒𝑟
𝑁𝑈𝑃+
: = 𝑚𝑎𝑥 ෍
𝑖=1
𝑁 𝑓𝑏
𝑁𝑈𝑃𝑖 , 0 , 𝑁 𝐷𝑒𝑟 = ෍
𝑖=1
𝑁 𝑓𝑏
𝑁𝑖 , 𝐹𝑉 = ෍
𝑖=1
𝑁 𝑓𝑏
𝐹𝑉𝑖 .

3: Regulation
EBA RTS: fall-back approach [2/2]
Example of AVA
calculation under the
fall-back approach. We
assume to apply the
Fall-Back approach to
the 1% portion of the
previous core portfolio.
The net unrealized
P&Ls are the 0.1% of
the fair values, positive
for derivatives and
negative for bonds. The
notional for derivatives
is assumed 10 times
the fair value. The AVA
Fall-Back is then
summed to the
remaining 99% of the
previous AVA core to
obtain the total AVA.

 The core approach is mandatory only for institutions above the threshold of €15 bln.
 Institutions below the threshold may choose between simplified and core approaches.
 Which one is more convenient (generate smaller capital absorption) ?
There is no precise mathematical relation between the simplified and core AVAs.
The actual figures depend principally on the actual positions
included in the prudent valuation scope.
3: Regulation
Simplified vs core approaches [1/2]

3: Regulation
Global view of key regulatory concepts
Fair
value
CRR art. 34, 105
EBA RTS
Prudent
value
Scope
90% confidence level
Simplified approach
Mark to market
Mark to model
IPV
Systems
and
controls
Core approach
Expert based
Fall back
Diversification
0.1% Formula
9 AVAs

3: Regulation
AVAs vs XVAs
Simple question, difficult answer
Should XVAs be included into the prudent valuations scope ?
Let’s look atthe state of the art...
...and try some forecast
XVA Accounting standards Accounting practice
CVA, DVA YES, both IFRS13 and GAAP mention
about counterparty and own credit
risk.
Some news on DVA expected
YES, CVA and DVA are normally included
into accounting fair value and reported in
public balance sheet disclosures
FVA NO, at least not explicitly YES, most banks have included FVA into
accounting fair value and report some
(scarce) information in public balance
sheet disclosures
MVA NO, see recent survey NO, see recent survey and public balance
sheet disclosures
KVA NO, see Kenyon&Kenyon, Risk Mag.
Mar. 2016
NO, see recent survey
xxxVA Who knows...
NEW

Recently, two regulators proposed a consultation on enhancements to the reporting of
prudent valuation figures.
 The industry (ISDA, IIF, AFME, etc.) is actively discussing the proposed template and
comments to BCBS are expected. Main issues are the following:
o Partial overlapping and consistency of AVA definitions under BCBS and EBA RTS
o Different AVA scopes of applications, since EBA RTS allows for many exclusions.
o AVAs break down by asset class is problematic for EU Institutions because EBA RTS
requires AVA calculation at valuation exposure level. For example, AVA MPU for some
risk factor (e.g. IR/vols and FX rates/vols) naturally include multiple asset classes.
1. BCBS Consultative Document, “Pillar 3 disclosure requirements –
consolidated and enhanced framework”, March 2016, issued for
comment by 10 June 2016.
 Template PV1, in particular, aims to disclose prudent valuation
figures under Pillar 3, consistently with previous BCBS
requirements:
o BCBS “International Convergence of Capital Measurement and
Capital Standards” (Basel 2, comprehensive version) June 2006,
paragraphs 698-701.
o BCBS “Supervisory guidance for assessing banks’ financial
instrument fair value practices”, April 2009 (in particular Principle
10).
3: Regulation
Prudent valuation reporting [1/3]
NEW

Template PV1 proposed in BCBS Consultative Document,
“Pillar 3 disclosure requirements – consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016.
3: Regulation
NEW

2. EBA consultation paper (EBA/CP/2016/02), ”Draft
implementing Technical Standards amending Commission
Implementing Regulation (EU) 680/2014 on supervisory
reporting of institutions”, 4 March 2016, issued for comment
by 31 March 2016.
The proposed amendement of prudent valuation
supervisory reporting is articulated into four new templates.
 Template C 32.01: fair valued asset and liabilities
o Rows: accounting categorisation (HFT, AFS, etc.)
o Columns: fair value amounts of inclusions and
exclusions according to EBA RTS
 Template C 32.02: core approach
o Rows: break down by portfolio/trade class (vanilla/exotic), diversification benefit, fall back app.
o Columns: AVAs and fair value adjustments according to EBA RTS.
 Template C 32.03: focus on AVA MoRi
 Template C 32.01: focus on AVA CoPo
Main issues are the following:
 breakdown by portfolio/trade class (vanilla/exotic) is not consistent with AVA calculation by
valuation exposures,
 amount of data required
3: Regulation
NEW

FV under prudent valuation scope = FV asset & liabilities – FV under prudential filters
3: Regulation
Prudent valuation data: QIS [1/3]

 The EBA conducted a QIS to estimate the total impact of the requirements of the RTS
including 59 banks across 15 jurisdictions, with the following results.
 Small banks: < 15 €/bln
 Medium banks: 15 - 100 €/bln
 Large banks: > 100 €/bln
Average
227 €/mln
per bank
3: Regulation

According to EBA: [*]
 approximately 6,500 credit institutions across EEA Member States (as of 2013) report
supervisory data to their respective competent authorities.
 Total value of assets: approximately EUR 42,000 billion.
 Approximately 750 institutions (11%) are above the EUR 15 billion threshold.
[*] European Banking Authority, Consultation Paper, “Draft Implementing Technical Standards amending
Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016,
https://www.eba.europa.eu/-/eba-seeks-comments-on-reporting-of-prudent-valuation-
information
3: Regulation

3: Regulation
Prudent valuation data: 2014-2015 [1/3]
Source: elaboration of public data (in collaboration with Ernst Young).
NEW

3: Regulation
Source: elaboration of public data (in collaboration with Ernst Young).
NEW

Comments
 Fair value is given by FV assets + FV liablities including
o Held for trading (HFT)
o Fair Value Option (FVO)
o Hedging Derivatives (HD)
o Available For Sale (AFS)
 Fair value for prudent valuation has been estimated from fair value excluding HD and
AFS (100%, no AFS filters applied, slightly underestimated).
 AVA/CET1 figures are rather different, ranging from negligible to important %.
 AVA core / AVA simplified > 1 in a few cases, thus AVA simplified is neither an AVA
cap nor an AVA floor.
 Prudent valuation not driven by L3 instruments: moving from AVA/L3 to AVA /(L2+L3)
changes the figures by a factor of 100.
 2014-2015 average AVAs double the 2013 QIS result (500 vs 227 mln€).
3: Regulation
NEW

1. XVAs
3: Regulation
Prudent valuation data: survey [1/4]
 Restricted access to clients only
 Dec.2015
 30 respondents (18 GSIBs, 15 UK)
 60 questions
 EBA RTS not yet in place at the time
 One third does not account FVA in fair
value, more than half does account AVA
IFC in prudent value.
 MVA and KVA are not accounted both in
fair and prudent values.
NEW

1. XVAs (cont’d)
3: Regulation
 Only 30% use a spread term structure
 «Peer estimate» is a possible answer to
the question «what is an exit price for
FVA ?»
 Possible use of Markit XVA service
 Both funding spreads sources and term
structures vary considerably, both for
FVA (Fair Value) and for AVA IFC
(prudent value)
NEW

2. P&L variance test
3: Regulation
 The P&L variance test is difficult to run
and pass in case of many relevant risk
factors, and may lead to huge AVA MPU.
 60% ignore the P&Lvariance test
 Only 7% run extensive application
 Only 14% apply with quarterly frequency
NEW

3. Other
3: Regulation
 One half does apply/does not apply
offsetting between AVAs and other
regulatory capital reserves.
 Possible offsets should be clarified, to
avoid possible capital double countings.
 One third reduces the valuation
exposure.
NEW

4. AVA calculation
o Definitions and basic assumptions
o Market price uncertainty AVA
o Close-out costs AVA
o Model risk AVA
o Unearned credit spreads AVA
o Investing and funding costs AVA
o Concentrated positions AVA
o Future administrative costs AVA
o Early termination AVA
o Operational risk AVA
o Case studies & examples
Summary

4: AVA calculation
Definitions and basic assumptions [1]
In other words, a valuation position will display valuation exposures to its valuation
inputs. Clearly the degree of valuation exposure to a valuation input depends on the
particular valuation position.
Definitions (EBA RTS art. 2)
Item Definition Example
Valuation
position
A portfolio of financial instruments or
commodities measured at fair value, held in
both trading and non-trading books
E.g. a portfolio of
derivatives
Valuation
input
A set of parameters (observable or non-
observable) that influences the fair value of a
valuation position
E.g. yield curve,volatility
cube, market/historical
correlations, prepayment,
etc.
Valuation
exposure
The amount of a valuation position which is
sensitive to the change in a valuation input
E.g. the trades in portfolio
above sensible to the
valuation inputs above.

4: AVA calculation
Fair value
In general, we denote the fair value of a valuation position 𝑝𝑖 at time t with 𝐹𝑉 𝑡, 𝑝𝑖 or,
shortly, with 𝐹𝑉𝑖 𝑡 , with 𝑖 = 1, … , 𝑁 𝑝. Given a set of valuation positions subject to
prudent valuation, we denote the total fair value as
𝐹𝑉 𝑡 = ෍
𝑖=1
𝑁 𝑝
𝐹𝑉𝑖 𝑡
In the context of prudent valuation, we consider the following properties of fair value FV.
 FV is positive for assets (𝐹𝑉𝑖 𝑡 > 0) and negative for liabilities (𝐹𝑉𝑖 𝑡 < 0).
 Financial institutions have appropriate internal IPV process in place (EBA RTS, p. 7).
 FV is computed by the institution consistently with the applicable financial reporting
standards, e.g. IFRS13, and with its internal fair value policy.
 The institution possibly applies and reports a number of valuation adjustments to the
FV, according to its internal fair value policy.

4: AVA calculation
Fair value (cont’d)
 The FV of a valuation position may be subject to the sources of uncertainty
mentioned in the CRR, art. 105.10-11, and thus associated to a specific AVA under
the core approach described in the EBA RTS.
 According to EBA RTS art. 8.3, the FV of a valuation position associated to a specific
AVA under the core approach must include all the fair value adjustments possibly
applied by the institution associated to the same source of valuation uncertainty as
the specific AVA. In case a fair value adjustment cannot be associated to the same
source of valuation uncertainty of a specific AVA, it must not be included in the FV for
the specific AVA calculation. In case of impossible association with any AVA, the fair
value adjustment cannot be included at all in the prudent valuations scope.

4: AVA calculation
 Fair value for derivatives
In general, we may consider the fair value for derivatives split into various
components,
𝐹𝑉 𝑡 = 𝑉0 𝑡 + 𝑉𝐴𝑑𝑗 𝑡
𝑉𝐴𝑑𝑗 𝑡 = 𝑉𝑏𝐶𝑉𝐴 𝑡 + 𝑉𝐹𝑉𝐴 𝑡 + 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 + 𝑉 𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 + ⋯
where
o 𝑉0 𝑡 is the “base” fair value component at valuation time t, as if the contract were
covered by a perfect CSA;
o the other components gathered in 𝑉𝐴𝑑𝑗 𝑡 corresponds to the value of the various
risk components underlying the financial instrument, such as the bilateral
counterparty risk 𝑉𝑏𝐶𝑉𝐴 𝑡 , funding risk 𝑉𝐹𝑉𝐴 𝑡 , bid-ask 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 , model risk
𝑉 𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 , etc. Such components may be considered or not in the FV or in in
𝑉𝐴𝑑𝑗 𝑡 according to the fair value policy of the institution.

4: AVA calculation
 Fair value for securities
We consider the fair value for securities, instead, as a single value, without splitting
into distinct components. In other words, the value of the various risk components is
included in the credit spread associated to the security.

4: AVA calculation
Valuation input
 The FV of a valuation position 𝑝𝑖 depends on its valuation inputs, denoted with
𝑢𝑗, 𝑗 = 1, … , 𝑁 𝑢,
 The FV may be also denoted as 𝐹𝑉(𝑡, 𝑝𝑖, 𝑢1, … , 𝑢 𝑁 𝑢
). We stress that different
valuation positions depend, in general, on different valuation inputs.
 The valuation input 𝑢𝑗 is associated to a single elementary risk factor, or source of
valuation uncertainty.

4: AVA calculation
Valuation exposure
 The valuation exposure of a valuation position 𝑝𝑖 to the valuation input 𝑢𝑗 is the
amount of that valuation position which is sensitive to the change in the valuation
input 𝑢𝑗.
 The valuation exposure can be also associated to the sensitivity of the valuation
position 𝑝𝑖 to the valuation input 𝑢𝑗.
 In a wider sense, the valuation exposure is anything that measures the dependency
of the FV of the valuation position 𝑝𝑖 to the valuation input 𝑢𝑗.

4: AVA calculation
Prudent value
 We denote the prudent value of category k for a valuation position 𝑝𝑖 associated to
the source of valuation uncertainty 𝑢𝑗 at time t with 𝑃𝑉 (𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘) or, shortly, with
𝑃𝑉𝑖𝑗𝑘 𝑡 , with 𝑗 = 1, … , 𝑁 𝑢 and 𝑘 = 1, … , 𝑁𝐴𝑉𝐴. The category is the AVA type (MPU,
CoCo, etc…).
 Degree of certainty
The CRR (article 105.1) requires a prudent value that achieves an “… appropriate
degree of certainty”. The EBA RTS specifies the appropriate degree of certainty as
follows.
o AVA MPU, CoCo e MoRi (art. 9-11):
• where possible, the prudent value of a position is linked to a range of
plausible values and a specified target level of certainty (90%);
• in all other cases, an expert-based approach is allowed, using qualitative
and quantitative information available to achieve an equivalent level of
certainty as above (90%).
o AVA UCS and IFC (art. 12-13): these AVAs must be split into their MPU, CoCo
and MoRi components, and aggregated to the corresponding MPU, CoCo and
MoRi AVAs, respectively. Thus, the same level of certainty in the prudent value
(90%) must be statistically achieved.

4: AVA calculation
Prudent value (cont’d)
o Other AVAs (CoPo, FAC, ET, OpR, art. 14-17): it must be statistically achieved
the same level of certainty in the prudent value (90%) as for the previous AVAs
(art. 8.3).
o For positions where there is valuation uncertainty but it is not possible to
statistically achieve a specified level of certainty, the same target degree of
certainty in the prudent value (90%) is required.
o “The EBA accepts that for the majority of positions where there is valuation
uncertainty, it is not possible to statistically achieve a specified level of
certainty; however, specifying a target level is believed to be the most
appropriate way to achieve greater consistency in the interpretation of a
“prudent’ value”.”
In conclusion, the same degree of certainty in the prudent value (90%)
must be achieved for all AVAs.

4: AVA calculation
Prudent value (cont’d)
o Notice that, by definition, the prudent value is always equal to or lower than the
fair value, both for assets and liabilities. Taking into account the FV definition
above we have, for both assets and liabilities,
𝑃𝑉𝑖𝑗𝑘 𝑡 ≤ 𝐹𝑉𝑖 𝑡 ∀ 𝑖 = 1, … , 𝑁 𝑝, 𝑗 = 1, … , 𝑁 𝑢, 𝑘 = 1, … , 𝑁𝐴𝑉𝐴
o Hence, PV is generally positive for assets (𝑃𝑉𝑖𝑗𝑘 𝑡 > 0) and negative for
liabilities (𝑃𝑉𝑖𝑗𝑘 𝑡 < 0). This is not strictly true in all cases, since some asset
(e.g. an OTC swap) may have positive FV and negative PV (not viceversa).

4: AVA calculation
Additional Valuation Adjustment (AVA)
 Simplified approach
Given the total fair value of assets and liabilities, 𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 𝑡 > 0, 𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑡 < 0,
the total AVA under the simplified approach is given by the following expression
𝐴𝑉𝐴 𝑡 = 0.1% × 𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 + 𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
where
𝐹𝑉𝐴𝑠𝑠𝑒𝑡𝑠 ≔ ෍
𝑖=1
𝑁 𝐴𝑠𝑠𝑒𝑡𝑠
𝐹𝑉𝑖 𝑡 ,
𝐹𝑉𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 ≔ ෍
𝑖=1
𝑁 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝐹𝑉𝑖 𝑡 .

4: AVA calculation
Additional Valuation Adjustment (AVA) (cont’d)
 Core approach
Given the fair value of a valuation position 𝑝𝑖, 𝐹𝑉𝑖 𝑡 , and the corresponding prudent
value of category k associated to the source of valuation uncertainty 𝑢𝑗, 𝑃𝑉𝑖𝑗𝑘 𝑡 , the
AVA under the core approach is given by the following expressions
𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 : = 𝑤 𝑘 𝐹𝑉 𝑡, 𝑝𝑖 − 𝑃𝑉 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 ,
𝐴𝑉𝐴 𝑡, 𝑘 : = ෍
𝑖=1
𝑁 𝑝
෍
𝑗=1
𝑁 𝑢
𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 ,
where:
o 𝑤 𝑘 is the aggregation weight, such that 𝒘 = 0.5,0.5,0.5,1,1,1,1 for the seven
AVAs MPU, CoCo, MoRi, CoPo, FAC, ET, OpR, respectively.
o 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 ≔ 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 is the k-th AVA for valuation position 𝑝𝑖 and source
of valuation uncertainty 𝑢𝑗 at time t, weighted for aggregation;
o 𝐴𝑉𝐴 𝑡, 𝑘 is the total k-th category level AVA associated to all relevant sources of
valuation uncertainty 𝑢1, … , 𝑢 𝑁 𝑢
and valuation positions 𝑝1, … , 𝑝 𝑁 𝑝
. Also this AVA is
already weighted for aggregation by construction of 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 .

4: AVA calculation
Notice that:
 𝐴𝑉𝐴 𝑘 𝑡 always include the aggregation weight 𝑤 𝑘 at any level (valuation exposure,
total AVA, total PVA);
 𝐴𝑉𝐴 𝑘 𝑡 ≥ 0 ∀ 𝑘 at any level (valuation exposure, total AVA, total PVA), both pre and
post aggregation;
 𝐴𝑉𝐴 𝑘 𝑡 = 0 when the fair value is already prudent w.r.t. the 𝐴𝑉𝐴𝑗 source of valuation
uncertainty, 𝐹𝑉𝑖 𝑡 = 𝑃𝑉𝑖𝑗𝑘 𝑡 ;
 the previous expressions holds both for assets (𝐹𝑉i 𝑡 > 0) and liabilities (𝐹𝑉i 𝑡 <
0).

4: AVA calculation
AVA for derivatives
 Remind that for derivatives the total value may be split across different components
𝐹𝑉 𝑡 = 𝑉0 𝑡 + 𝑉𝐴𝑑𝑗 𝑡
𝑉𝐴𝑑𝑗 𝑡 = 𝑉𝑏𝐶𝑉𝐴 𝑡 + 𝑉𝐹𝑉𝐴 𝑡 + 𝑉𝐵𝑖𝑑𝐴𝑠𝑘 𝑡 + 𝑉 𝑀𝑜𝑑𝑒𝑙𝑅𝑖𝑠𝑘 𝑡 + ⋯
 We assume that such components are not strongly correlated. In particular, we
assume that the market value is not strongly correlated with credit and funding risk.
 In this case, also the AVAs results to be split across the same components
𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 = 𝐴𝑃𝑉𝐴0 𝑡, 𝑝𝑖, 𝑢𝑗, 𝑘 + 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝐶𝑉𝐴 + 𝐴𝑃𝑉𝐴 𝑡, 𝑝𝑖, 𝑢𝑗, 𝐹𝑉𝐴 + ⋯

4: AVA calculation
Prudent Valuation Adjustment (PVA)
The total Prudent Valuation Adjustment (PVA), to be deduced from the CET1, is
computed as follows.
𝑃𝑉𝐴 𝑡 ≔
𝐴𝑉𝐴(𝑡) Simplified approach,
෍
𝑘=1
𝑁 𝐴𝑉𝐴
𝐴𝑉𝐴 𝑘 𝑡 Core approach.
The detailed AVA aggregation rules under the core approach are discussed within the
detailed AVA calculation rules in the following.

4: AVA calculation
AVA aggregation
The total AVA under the core approach is computed using the following algorithm.
 CoPo, FAC, EaT, OpR AVAs are aggregated each as the sum of its corresponding
individual components at valuation positions level, each weighted at 100%.
 UCS and IFC AVAs are decomposed each into 3 components related to MPU, CoCo
and MoRi uncertainties, which are taken into account in the total MPU, CoCo and
MoRi AVA aggregation discussed below.
 MPU, CoCo and MoRi AVAS are aggregated each as the sum of:
o its individual components at valuation positions level
o the corresponding UCS and IFC AVA contributions above,
o all weighted at 50%.
 The total AVA is computed as the simple sum of the residual MPU, CoCo, MoRi,
CoPo FAC, EaT, OpR AVAs determined above.
In conclusion, the final aggregation includes 50% of MPU, MoRi, CoCo, UCS and IFC
AVAs (5 out of 9), and 100% of CoPo FAC, EaT, OpR AVAs (4 out of 9).

4: AVA calculation
Definitions summary
Item Definition Comments
Fair value 𝐹𝑉 𝑡 = ෍
𝑖=1
𝑁 𝑝
𝐹𝑉𝑖 𝑡 i = index for valuation positions
Prudent Value
𝑃𝑉𝑖𝑗𝑘 𝑡 ≤ 𝐹𝑉𝑖 𝑡
∀ 𝑖 = 1, … , 𝑁 𝑝, 𝑗 = 1, … , 𝑁 𝑢, ∀ 𝑘 = 1, … , 𝑁𝐴𝑉𝐴
o j = index for risk factors
o k = index for AVAs
Additional
Valuation
Adjustment
(simplified)
𝐴𝑉𝐴 𝑡 = 0.1% ෍
𝑖=1
𝑁 𝐴𝑠𝑠𝑒𝑡𝑠
𝐹𝑉𝑖 𝑡 + ෍
𝑖=1
𝑁 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝐹𝑉𝑖 𝑡
𝐴𝑉𝐴 𝑡 is the total valuation
adjustment at time t
Additional
Valuation
Adjustment
(core)
𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 ∶= 𝑤 𝑘 𝐹𝑉𝑖 𝑡 − 𝑃𝑉𝑖𝑗𝑘 𝑡 ,
𝐴𝑉𝐴 𝑘 𝑡 : = ෍
𝑖=1
𝑁 𝑝
෍
𝑗=1
𝑁 𝑢
𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡
o 𝐴𝑃𝑉𝐴𝑖𝑗𝑘 𝑡 is the k-th AVA
associated to source of
valuation uncertainty j and
valuation position i at time t,
o 𝐴𝑉𝐴 𝑘 𝑡 is the total k-th AVA at t
Prudent
Valuation
Adjustment
𝑃𝑉𝐴 𝑡 ≔
𝐴𝑉𝐴(𝑡) Simplified
෍
𝑘=1
𝑁 𝐴𝑉𝐴
𝐴𝑉𝐴 𝑘 𝑡 Core
𝑃𝑉𝐴 𝑡 is the total valuation
adjustment at time t

Price distribution, fair value, fair value adjustment, prudent value, AVA
What about real
price distributions...?
Fair value
(mean)Fair value
adjusted
Prudent value
(quantile)
Fair value adjustment
AVA
4: AVA calculation

4: AVA calculation
Data sources
Market
based
Data sourcing
(EBA RTS Art. 3)
Expert
based
Consensus service data
Proxy data based on similar instruments
Application of prudent shifts to valuation inputs
Exchange prices in a liquid market
Trades in the exact same or very similar instrument,
either from internal records or from the market
Tradable quotes from brokers and other market
participants
Identification of natural bounds to the value of an
instrument
Indicative broker quotes
Counterparty collateral valuations

4: AVA calculation
AVA discussion scheme
Since AVAs are rather involved and diversified, we need to discuss each AVA using a
fixed scheme, including:
 AVA definition and regulatory references
 AVA scope of application
 Fair Value related to the AVA
 AVA calculation scheme
 Examples
 Applications

4: AVA calculation
AVA Market Price Uncertainty (MPU) [1]
 AVA definition
AVA Market Price Uncertainty (MPU) refers to the valuation uncertainty of a valuation
exposure arising from uncertainty of a valuation input.
This kind of uncertainty is rather common in price evaluation and may appear in
different situations, for example:
o when the financial instrument is marked to market (e.g. a bond listed), and there
are multiple reliable price contributors;
o when the financial instrument is marked to model using some valuation input (e.g.
an OTC IRS valued using multiple yield curves based on IRS market quotes), and
there are multiple price contributors for the valuation inputs (e.g. multiple IRS
market makers).
 AVA main references
o EBA RTS, article 9.
o EBA FAQs 6.1, 21, 23, 23.1, 28, 30, 31, 40.1, 40.3.

4: AVA calculation
Within the general prudent valuation scope (see before), AVA MPU regards in
particular those valuation positions without either a firm tradable price, or a price that
can be determined from reliable data based on a liquid two-way market, and such
that at least one valuation input has material valuation uncertainty.
AVA MPU shall be computed for all valuation positions 𝑝𝑖, 𝑖 = 1, … , 𝑁 𝑝 showing a
valuation exposure to a valuation input 𝑢𝑗, 𝑗 = 1, … , 𝑁 𝑢 (valuation exposure level).
We stress that a single valuation position 𝑝𝑖 may show a valuation exposure to either
none, or one, or a few, or many, or all valuation inputs 𝑢𝑗. Thus we may have
A𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗1
= 0 and 𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗2
≠ 0 for the same valuation position
𝑝𝑖 and two different valuation inputs 𝑢𝑗1
≠ 𝑢𝑗2
.
 AVA Fair Value
The FV of the trades subject to AVA MPU may include or not the effect of possible
MPU. In some particular cases, Institutions may account FV adjustments in their
balance sheets to cover possible losses related to MPU. In this case the FV subject
to prudent valuation for AVA MPU must include these FV adjustments, or, in other
words, such FV adjustments must be subtracted from the AVA MPU (keeping the AVA
non-negative).

4: AVA calculation
Does the valuation position have a valuation
exposure 𝑝𝑖, 𝑖 = 1, … , 𝑁𝑝, to uncertainty of
valuation inputs 𝑢𝑗, 𝑗 = 1, … , 𝑁 𝑢?
o Is there firm evidence of a tradable price for the valuation
exposure 𝑝𝑖 ?
o Or can the price for the valuation exposure 𝑝𝑖 be determined
from reliable data based on a liquid two-way market (as
defined in art. 338 of CRR) ?
𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 = 0
YES
Compute individual 𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗
for each valuation exposure 𝑝𝑖 to
each valuation input 𝑢𝑗
Do sources of market
data indicate no
material valuation
uncertainty ?
YES
YES
NO
NO
AVA Market Price Uncertainty (MPU) (EBA RTS, article 9) refers to the valuation uncertainty of a
valuation exposure arising from uncertainty of a valuation input.
NO
Continue

4: AVA calculation
o Use the data sources defined in Art. 3.
o Calculate AVAs on valuation exposures 𝑝𝑖 related to each valuation input 𝑢𝑗 used in the
relevant valuation model.
o For non-derivative valuation positions, or derivative positions which are marked to market,
refer to the instrument price, or decompose into each valuation input required to calculate
the exit price, treated separately.
o If a valuation input 𝑢𝑗 consists of a (D-dimensional) matrix of parameters, 𝑢𝑗
𝛼𝛽𝛾…
, calculate
𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 based on the valuation exposures related to each matrix element 𝑢𝑗
𝛼𝛽𝛾…
.
o If a valuation input 𝑢𝑗 does not refer to tradable instruments, map the valuation input and
the related valuation exposure to a set of market tradable instruments.
Do you reduce the number
of parameters of the
valuation input 𝑢𝑗 (D-dim.
matrix) for the purpose of
calculating AVAs ?
Continue
NO
P&L
variance
test
Positive
YES
Negative
Subject to independent
control function review
and internal validation on
at least an annual basis

4: AVA calculation
Estimate a point
ො𝑢𝑗 within the
range with 90%
confidence to exit
the valuation
exposure at that
price or better.
Use expert-based
approach using
qualitative and
quantitative
information
available to achieve
a prudent value ො𝑢𝑗
with confidence
level equivalent to
90%.
Do sufficient data exists to
construct a range of
plausible values for a
valuation input 𝑢𝑗?
YES
NO
Notify competent
authorities of the
valuation
exposures for
which this
approach is
applied, and the
methodology used
to determine the
AVA.
Estimate a point
ො𝑢𝑗 within the
range with 90%
confidence that
the mid value that
could be achieved
in exiting the
valuation
exposure would
be at that price or
better.
Continue
Is the range of
plausible values
of 𝑢𝑗 is based on
exit prices ?
Is the range of
plausible values
of 𝑢𝑗 is based on
mid prices ?
NO
YES

4: AVA calculation
Compute individual AVA MPU
𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 = 𝑤 𝑀𝑃𝑈 𝐹𝑉 𝑡, 𝑝𝑖, 𝑢𝑗 − 𝑃𝑉 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗
Apply the valuation input uncertainties ො𝑢𝑗 to valuation
exposures 𝑝𝑖 and compute prudent value MPUs
By revaluation:
𝑃𝑉 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 = 𝐹𝑉 𝑀𝑃𝑈 𝑡, 𝑝𝑖, ො𝑢𝑗
or (when the uncertain input is the
instrument price):
𝑃𝑉 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 = ො𝑢𝑗
By exposure
𝑃𝑉 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗 = 𝐹𝑉 𝑡, 𝑝𝑖, 𝑢𝑗 −
𝜕𝐹𝑉
𝜕𝑢𝑗
ො𝑢𝑗 − 𝑢𝑗
Compute total category level AVA MPU
𝐴𝑉𝐴 𝑀𝑃𝑈 𝑡 = ෍
𝑖=1
𝑁 𝑝
෍
𝑗=1
𝑁 𝑢
𝐴𝑃𝑉𝐴 𝑀𝑃𝑈 𝑡, 𝑝𝑖, 𝑢𝑗

4: AVA calculation
 AVA calculation
o Securities
• Impaired/defaulted securities
𝐴𝑉𝐴 𝑀𝑃𝑈 𝑡 = 0 if the FV is already conservative and does not depend on
uncertain market data, otherwise go to next cases.
• Liquid securities accounted at Fair Value Level 1
𝐴𝑉𝐴 𝑀𝑃𝑈 𝑡 = 0, if the FV is calculated on market tradable prices with negligible
bid-ask, otherwise go to next cases.
• Contributed securities accounted at Fair Value Level 1
a possible approach is
A𝑉𝐴 𝑀𝑃𝑈 𝑡 = 𝑤 𝑀𝑃𝑈 ൝
+0.9 × 𝐹𝑉 𝑡 − 𝑉𝑏𝑖𝑑
𝑚𝑖𝑛
𝑡 long positions,
−0.9 × 𝐹𝑉 𝑡 − 𝑉𝑎𝑠𝑘
𝑚𝑎𝑥
𝑡 short positions.
where 𝑉𝑏𝑖𝑑
𝑚𝑖𝑛
𝑡 /𝑉𝑏𝑖𝑑
𝑚𝑖𝑛
𝑡 are the lowest/highest bid/ask prices quoted at time t,
and 𝑤 𝑀𝑃𝑈 = 0.5.
• Securities accounted at Fair Value Level 2 or 3
AVA MPU shall be computed via sensitivity or full revaluation based on relevant
risk factors, in particular credit spread and interest rate curves, using prudent
MPUs.

4: AVA calculation
 AVA calculation (cont’d)
o Derivatives
AVA MPU is computed via sensitivity or full revaluation based on relevant risk
factors.
 MPU estimation
AVA MPU calculation is based on the estimation of MPUs of relevant (possibly all)
risk factors, including volatilities and correlations.
Possible sources of MPUs are the following.
o Front office traders active in their respective markets.
o Appropriate selection of multiple contributors (brokers, market makers) available
from data providers (i.e. Bloomberg or Reuters).
o Consensus price services (e.g. Markit).
o Collateral counterparty valuations for derivatives.
o Historical series of prices and market data

4: AVA calculation
 Examples
o Bond for which there exist multiple price contributors.
o IRS valued using multiple yield curves based on market quotations (Fras, Futures,
OIS, IRS, Basis IRS, etc.) for which there exist multiple market makers.

4: AVA calculation
Case study of AVA MPU calculation for a security.
• Top left: market bid and ask prices. FV is
computed as average mid price = 162.25.
• Bottom left: ranking and percentiles of mid prices,
AVA MPU for long and short positions, equal to
0.14 and 0.12, respectively.
• Top right: distribution chart.

4: AVA calculation
Examples with sensitivities.
See EBA RTS sec. 4.1.1 and ref. [23].

4: AVA calculation
P&L variance test
Notation
 𝑅𝑖𝑗, 𝑖 = 1, … , 𝑁 𝑅, 𝑗 = 0, … , 𝑁 𝑑 = i-th risk factor (scalar, vector or matrix element,
generically indexed by i with some ordering) for j-th date (backward time ordered, j =
0 = today, j = 1 = yesterday business day, etc….).
 Δ𝑅𝑖𝑗 ≔ 𝑅𝑖𝑗 − 𝑅𝑖𝑗−1 = j-th daily variation of risk factor 𝑅𝑖𝑗.
 𝑉𝑗 = fair value of today’s valuation exposure at j-th date (static portfolio).
 𝛿𝑖𝑗 ≔ Τ𝜕𝑉𝑗 𝜕𝑅𝑖𝑗 = first-order sensitivity of today’s valuation exposure to risk factor 𝑅𝑖𝑗
(delta, vega, rho, etc.).
Discussion
We know the valuation exposure and its fair value at today’s date, 𝑉0. Instead, it’s much
more difficult to recompute the past fair values of the present valuation exposure,
𝑉1, … , 𝑉𝑁 𝑑
. Thus, we approximate such values using first order Taylor expansion and
today’s risk factors sensitivities as follows
𝑉𝑗 ≅ 𝑉𝑗−1 + ෍
𝑖=1
𝑁 𝑅
𝛿𝑖𝑗 Δ𝑅𝑖𝑗 + ⋯ ≅ 𝑉𝑗−1 + ෍
𝑖=1
𝑁 𝑅
𝛿𝑖,0 Δ𝑅𝑖𝑗.

4: AVA calculation
P&L variance test (cont’d)
Notice that we’re assuming that first order sensitivities are fairly constant w.r.t. the risk
factors levels, 𝛿𝑖,𝑗 ≅ 𝛿𝑖,0 ∀ 𝑗. This is consistent with first order expansion and the static
portfolio assumption. Second order sensitivities (gamma in particular) can be introduced
in the Taylor expansion if required.
Hence we may define the j-th daily profit & loss of the valuation exposure as
𝑃𝐿𝑗: = 𝑉𝑗 − 𝑉𝑗−1 ≅ ෍
𝑖=1
𝑁 𝑅
𝛿𝑖,0 Δ𝑅𝑖𝑗, 𝑗 = 1, … , 𝑁 𝑑,
and we may compute the variance of the historical series as
𝑉𝑎𝑟 𝑃𝐿 = 𝑉𝑎𝑟 𝑃𝐿1, … , 𝑃𝐿 𝑁 𝑑
,
Where the EBA RTS requires 𝑁 𝑑 = 100.

4: AVA calculation
The calculations above may refer to both unreduced and reduced sets of risk factors as
well. Denoting reduced quantities with a hat, the reduced set is characterized by a lower
number of risk factors, ෡𝑁 𝑅 < 𝑁 𝑅. We may calculate the profit & loss of the reduced
valuation exposure as
෢𝑃𝐿𝑗: = ෠𝑉𝑗 − ෠𝑉𝑗−1 ≅ ෍
𝑖=1
෡𝑁 𝑅
መ𝛿𝑖,0 Δ𝑅𝑖𝑗, 𝑗 = 1, … , 𝑁 𝑑,
with the constrain on the total reduced and unreduced sensitivities,
෍
𝑖=1
෡𝑁 𝑅
መ𝛿𝑖,0 = ෍
𝑖=1
𝑁 𝑅
𝛿𝑖,0 ,
for each single risk factor class (e.g. delta, vega, etc.).

4: AVA calculation
Finally, the P&L variance ratio test required by EBA RTS [1], art. 9 can be calculated as
𝑃𝐿 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑟𝑎𝑡𝑖𝑜 =
𝑉𝑎𝑟 𝑃𝐿 − ෢𝑃𝐿
𝑉𝑎𝑟 𝑃𝐿
≤ 0.1,
where
𝑉𝑎𝑟 𝑃𝐿 − ෢𝑃𝐿 = 𝑉𝑎𝑟 𝑃𝐿1 − ෢𝑃𝐿1, … , 𝑃𝐿 𝑁 𝑑
− ෢𝑃𝐿 𝑁 𝑑
.
Comments
The approach above is based on common approximations and requires, beyond the
present value and sensitivities of the valuation exposures, just the historical series of
the relevant market risk factors. The most important factor driving the result of the test is
obviously the choice of the reduced valuation exposure and it’s robustness over time.

4: AVA calculation
Possible issues
 How to define the unreduced set of risk factors ? -> choose the tradable nodes.
 How to choose the reduced set of risk factors ? This is arbitrary: in principle,
institutions are allowed, for each prudent valuation reporting date, to look for the
most convenient level of aggregation that minimizes the AVA and passes the test.
 How to ensure test stability from time to time ? The test success/failure strongly
depends on the distribution of the sensitivity w.r.t. the chosen level of aggregation.
Thus the same test applied to a dynamical portfolio may be positive one day and
negative another day.
Facts
Recent experience shows that:
 at least for some important cases (i.e. EUR interest rate yield curves and volatilities),
extreme aggregations onto a few (1-3) risk factors (pillar, pillar/strike) is often
sufficient to pass the test.
 Principal component analysis is helpful to understand the most important risk factors
and to select the possible aggregations to be tested.
 As a consequence, it seems that AVA MPU can be drastically reduced.
NEW

4: AVA calculation
AVA Close-Out Costs (CoCo) [1]
 AVA definition
AVA Close-Out Costs (CoCo) refers to the valuation uncertainty of a valuation
exposure arising from uncertainty in the exit price of the valuation positions, or, in
other terms, the cost of liquidity that a particular valuation exposure can exhibit in
particular market conditions. Both situations lead to relevant bid-ask spreads to exit
the valuation position.
Since illiquidity can also be seen as uncertainty around the mid price, AVA CoCo
overlaps with AVA MPU. Thus, when AVA MPU is based on tradable prices, AVA
CoCo may be set to zero.
 AVA main references
o EBA RTS, article 10.
o EBA FAQs 23, 24, 24.1, 28, 30, 31, 37, 37.1, 40.1, 40.3, 42.5.
Within the general prudent valuation scope (see before), AVA CoCo refers in
particular to those valuation positions for which there is not sufficient liquidity to exit
the valuation exposure at mid price (at 90% confidence level), and there are relevant
bid-ask spread.

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