Keywords: Specific risk, market risk, jump risk, jump diffusion, default risk
Abstract: 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
Full paper (218 KB PDF)
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Last update: April 26, 2001