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The Role Of Mathematical Models In The Current Financial Crisis Athula Alwis
1. Athula Alwis, Senior Vice President, Global Credit, Surety and
Political Risk Practice February 12, 2009
2. Robert Merton
“At times we can lose sight of the ultimate purpose of the models when their mathematics
become too interesting. The mathematics of financial models can be applied precisely, but
the models are not all precise in their application to the complex real world.
Their accuracy as a useful approximation to that world varies significantly across time
and place. The models should be applied in practice only tentatively, with careful
assessment of their limitations in each application.”
3. The Role of Mathematical Models in the Current
Financial Crisis – Lessons for the Export Credit and
Political Risk Business
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4. Agenda
I. Introduction
II. Liquidity Crisis
III. Credit Crisis
IV. Mortgage Crisis
V. History of Mathematical Modelling
VI. The Role of Models in the Current Crisis
VII. What can we learn?
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15. Liquidity Crisis
When an entity experiences a shortage of cash
To pay for day-to-day business operations (e.g., Payroll)
To meet debt obligations on time
To expand inventory and production
Does not necessarily mean that the business is insolvent
A specific liquidity risk!
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16. Liquidity Crisis
When businesses in general experience shortages of cash
Due to reduced lending by banks
Due to tighter lending standards by banks
Due to shortage of cash at banks
A liquidity crisis!
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17. Liquidity Crisis
Comparison to credit crisis
A sound business can experience a liquidity crisis by
temporary inaccessibility to required financing
A credit crisis is based on insolvency of entities
• Due to steep decline of previously over-priced assets
(mortgage-backed securities, CDO, etc)
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19. Credit Crisis
Widening of credit spreads
Increase in credit default rates
Weak corporate financials
Unstable capital bases
leading to…
A material reduction in available credit and / or
A significant increase in cost of credit
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20. Credit Crisis
Crisis of insolvency
Anticipated decline in value of collateral
Increased perception of risk
Change in monetary conditions
Loss of capital at banks
Lack of confidence in financial markets!
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24. Mortgage Crisis
The cost to economy
Recession
Lack of financing for solvent companies and individuals
with good credit
Over 2M job losses so far in the US in 2008 (4.5M
overall)
Over 2.8M unemployed in the UK
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25. Mortgage Crisis
The cost to financial institutions
Lack of confidence
• Bear Stearns and Merrill Lynch acquired
• Lehman Brothers – Chapter 11
• Washington Mutual acquired
• Goldman Sachs and J P Morgan became banks to survive
• Concerns at Citibank and AIG
• Issues at RBS
Lack of capital for growth
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27. Mortgage Crisis
Exacerbation of the credit cycle
Major corporate failures
High unemployment
Stagflation (inflation and economic stagnation)
Recession
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28. Mortgage Crisis – Perfect Storm
Liquidity crisis
Credit crisis
Mortgage crisis
Recession
It may not be over!
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30. Brief History of Credit Modeling
Ancient Romans traded options against outgoing cargo
from seaports
Charles Castelli (1877): Book titled “The Theory of Options
in Stocks and Shares”
Louis Bachelier (1900): Earliest known analytical valuation
for options in his mathematics dissertation at Sorbonne
Paul Samuelson (1955): Brownian Motion in the Stock
Market
Resource: A Study of Option Pricing Models, Kevin Rubash, Foster College of Business
Administration, Bradley University
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31. Brief History of Credit Modeling
Richard Kruizenga (1955): Put and Call Options: A
Theoretical and Market Analysis
James Boness (1962): A Theory and Measurement of Stock
Option Value
A clear theoretical improvement from previous work and a precursor to …
Black Scholes (1973): Option pricing Model
Resource: A Study of Option Pricing Models, Kevin Rubash, Foster College of Business
Administration, Bradley University
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32. Brief History of Credit Modeling
Fischer Black Myron Scholes Robert Merton
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33. Brief History of Credit Modeling
Robert Merton (1973): Relaxed the assumption of no
dividends
Jonathan Ingerson (1976): Relaxed the assumption of no
taxes or transaction costs
Robert Merton (1976): Relaxed the restriction of constant
interest rates
This is the beginning of structural modeling!
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34. Brief History of Credit Modeling
Vasicek – Kealhofer (1989): Modified Structural model
Jarrow – Turnbull (1995): Reduced Form model
Duffie – Singleton (1999): Improved Reduced Form model
David Li (2001): Incorporated a Gaussian Copula to tackle
correlation
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35. History of Mathematical Modeling
Benefits of Modeling
To be disciplined in risk selection and management
To be strategic in managing and growing the business
To compare against other businesses in terms of risk and
rewards
To measure and manage risk in a consistent manner
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36. History of Mathematical Modeling
Benefits of Modeling
To question and investigate assumptions, gut instincts and
“what if” scenarios
To assist in increasing shareholder value
To protect the franchise
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38. The Role of Models in the Current Crisis
A heavy reliance on mathematical models by banks,
investors and rating agencies
The use of inappropriate models to represent complex
market conditions
Over reliance on unrealistic models
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39. The Role of Models in the Current Crisis
Use of incorrect ratings from rating agencies
Improper calibration of models (lack of reliable data, wrong
assumptions, parameter error)
The mechanical use of models without properly
understanding underlying data, assumptions and
economic implications
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40. The Role of Models in the Current Crisis
Use of single metric to make decisions (For ex. Using VaR to
measure one boundary of risk)
Lack of awareness of boundaries/break points (for ex. real
estate values are bounded by income)
The limitations of models were not readily evident
Provided false confidence that encouraged additional risk
taking by practitioners
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41. The Role of Models in the Current Crisis
Lack of real world business experience by model
users/builders
Supported decision making solely based on past patterns
Models failed to capture liquidity risk, concentration risk,
correlation risk
Lack of appreciation for systemic risk and
interconnectedness of financial markets at moments of
extreme stress
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43. What Can We Learn
A mathematical model is a tool. It cannot and should not
replace the practitioner's experience, judgment and
business intuition. The major strategic decisions should
be guided by business knowledge and common sense of
experienced business leaders not by models.
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44. What Can We Learn
A model must reflect business realities as closely as
possible. Using inappropriate models mechanically
without exploring the applicability has been a serious
issue that must be addressed
Multiple metrics and models should be employed, if
possible (VaR, CTE, Volatility, Scenario Testing, …)
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45. What Can We Learn
The assumptions used in any model should be validated
by business practitioners. It is imperative that analysts
and modelers understand the market conditions,
coverage and business processes rather than
independently selecting assumptions for models in a
vacuum
The simplifying assumptions should be evaluated for
validity
Use actual original data (a clear advantage for the export
credit and political risk industry)
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46. What Can We Learn
The data that go into models should be validated,
scrubbed and compared to at least one other independent
source.
Regular review/upgrade of models and underlying
technologies has to be carried out
Model correlation (risk is not randomly distributed;
cannot escape it)
Consider systemic risk
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47. What Can We Learn
Mathematical tools cannot precisely model human
behavior
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48. • In preparing this presentation, W illis Re has relied upon data provided by external data
sources. N o attem pt has been m ade to independently verify the accuracy of this data.
W illis R e does not represent or otherw ise guarantee the accuracy or com pleteness of such
data, nor assum e responsibility for the result of any error or om ission in the data or other
m aterials gathered from any source in the preparation of this Presentation. W illis R e shall
have no liability in connection w ith results stem m ing from the analysis including but not
lim ited to any errors, om issions, inaccuracies, or inadequacies associated w ith the data.
W illis R e expressly disclaim s any and all liability to any third party in connection w ith
this presentation.
• In preparing this presentation, W illis Re has used procedures and assum ptions that W illis
R e believes are reasonable and appropriate. H ow ever, there are m any uncertainties
inherent in actuarial analyses. T hese include, but are not lim ited to, issues such as
lim itations in the available data, reliance on client data and outside data sources, the
underlying volatility of loss and other random processes, uncertainties that characterize
the application of professional judgm ent in estim ates and assum ptions, reinsurance
collectability, etc. U ltim ate losses, liabilities and claim s depend upon future contingent
events, including, but not lim ited to, unanticipated changes in inflation, law s, and
regulations. A s a result of these uncertainties, the actual outcom es could vary
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of any insurance or reinsurance program or venture, w hether or not such program or
venture applies the analysis or conclusions contained herein. Please consult your ow n
independent professional advisors before m aking any decisions related to any inform ation
contained herein.
• T his presentation is provided for inform ational purposes only; it is not intended to be
relied upon, and is not intended to be a com plete actuarial com m unication. A com plete
com m unication can be provided upon request. W illis Re actuaries are available to answ er
questions about this presentation.
• T he statem ents and opinions included in this presentation are those of the individual
speakers and do not necessarily represent the view s of W illis R e or its m anagem ent.
Disclaimer 48
