This document proposes using VaR (Value at Risk) models to forecast currency exchange rates for corporate advances that require quoting exchange rates up to 30 days in advance. Traditionally, VaR models focus only on potential losses, but this approach uses both upside and downside potential. It describes a historical simulation VaR model using 4 years of daily exchange rate data for over 90 currencies against the US dollar. The model provides exchange rate estimates at different confidence intervals for the forecast period. It has been backtested and can be extended to other uses like assessing pre-trade profitability. While VaR models have limitations, this represents an alternative application that leverages existing risk management infrastructure and processes.

1. CURRENCY FORECASTING
USING VAR
Exploring alternative applications of traditional Market Risk measurement

2. FROM RISK LIMITS TO VALUE GENERATION
• Traditionally VaR models have been used
to focus on only 1-tail of the loss
distribution
• It has been used as a measure to reflect
the risk ‘appetite’ of the institution
• This presentation explores an alternative
application of VaR utilizing both tails

3. CURRENCY FORECASTING – THE PROBLEM STATEMENT
• Corporate advances requires
quoting a Fx rate at inception of
the deal
• It could take anywhere from 2
to 30 days to close a typical
Currency advance
• Quoted Fx needs to incorporate
Volatility to protect margin

4. CURRENCY FORECASTING – USUAL APPROACH
• Multiple approaches available involving
Auto-regressive models, Macro-economic
based models, GBM based Fx Vol models
among others
• Often such approaches are a divergence to
stated risk policies of the bank in setting Fx
limits
• Involves separate modeling outside of risk
management and typically Economist cells

5. CURRENCY FORECASTING – AN ALTERNATIVE APPROACH
• As an alternate approach one could also use
the established VaR model and extend its
application
• Any VaR model could be employed – for this
illustration Historical simulation approach
was adopted
• VaR model chosen was un-weighted Historic
simulation over rolling 4years of daily Fx
Rates
• As with any other VaR based model, this
model also performed satisfactorily over the
shorter horizons of 1-2 months over ‘normal’
market periods

6. CURRENCY FORECASTING – THE SOLUTION
• The daily end of day (EOD) spot forex rates
vs USD for 90+ currencies were obtained
for the last 4 years
• An utility was created wherein user
chooses any currency pair and the forecast
period in days
• For any chosen forecast period, the utility
will calculate the VaR for various
confidence intervals using the ‘natural’ risk
horizon days
• For a chosen forecast horizon, the model
provides point estimates of “appreciation”
or “depreciation” at certain chosen levels
of significance

7. MODEL PERFORMANCE AND BACK-TESTING
• The model has been back-tested effectively
and benchmarked against the usual methods
and compared favorably
• This approach is an elegant extension of the
base VaR model that typically organizations
use and hence easier to execute and
document within broader risk policy
• Adoption of historical simulation facilitates
better communication to senior stakeholders
• Median prediction approach provides for
sufficient cushion against Fx volatility

8. FURTHER EXTENSIONS
• This approach can be further extended for
other use cases:
• Determine incremental VaR on the portfolio
and hence optimize counterparty that aids
maximum diversification benefit
• Estimate Intra-day VaR, a critical application
now for Intra-day large exposure movement
• Assess pre-trade profitability and impact on
initial margin

9. IN CONCLUSION
• As with any VaR model the limitations of this
model is consistent with limitations of VaR itself
• Basic premise of un-weighted historical simulation
approach is that past events have an equal
likelihood of occurrence in the future
• Tighter class intervals and weighting of
observations among the first things to look at
refinement within the aegis of historical simulation
approach of VaR modeling
• The purpose was to illustrate an alternative
application of VaR utilizing both tails of the
distribution function

10. KAUSTAV MUKHERJEE
MARKET RISK PRACTICE
Photo Credits: Shutterstock; Google Images; Pixabay
White Paper: Originally published in GARP, Nov 2013