Incorporating Event Risk into Value-at-Risk
Michael S. Gibson
Federal Reserve Board
FEDS Discussion Paper No. 2001-17
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.
Number of Pages in PDF File: 36
Keywords: Specific risk, market risk, jump risk, jump diffusion, default risk
JEL Classification: G10, G28working papers series
Date posted: May 4, 2001
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