Incorporating event risk into value-at-risk
Event risk is the risk that a portfolio's value can be affected by large jumps in market prices. Event risk is synonymous with "fat tails" or "jump risk". Event risk is one component of "specific risk", defined by bank supervisors as the component of market risk not driven by market-wide shocks. Standard Value-at-Risk (VaR) models used by banks to measure market risk do not do a good job of capturing event risk. In this paper, I discuss the issues involved in incorporating event risk into VaR. To illustrate these issues, I develop a VaR model that incorporates event risk, which I call the Jump-VaR model. The Jump-VaR model uses any standard VaR model to handle "ordinary" price fluctuations and grafts on a simple model of price jumps. The effect is to "fatten" the tails of the distribution of portfolio returns that is used to estimate VaR, thus increasing VaR. I note that regulatory capital could rise or fall when jumps are added, since the increase in VaR would be offset by a decline in the regulatory capital multiplier on specific risk from 4 to 3. In an empirical application, I use the Jump-VaR model to compute VaR for two equity portfolios. I note that, in practice, special attention must be paid to the issues of correlated jumps and double-counting of jumps. As expected, the estimates of VaR increase when jumps are added. In some cases, the increases are substantial. As expected, VaR increases by more for the portfolio with more specific risk.
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- Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer, vol. 12(2), pages 201-242, October.
- Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
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- Giovanni Barone‐Adesi & Kostas Giannopoulos & Les Vosper, 1999. "VaR without correlations for portfolios of derivative securities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(5), pages 583-602, 08.
- Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
- Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
- Duffee, Gregory R., 1995. "Stock returns and volatility A firm-level analysis," Journal of Financial Economics, Elsevier, vol. 37(3), pages 399-420, March.
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