Alternatives to the Standard Market Risk Model

In Chapters 2 through 5, we got pretty far using the standard model of jointly normally distributed asset or risk factor returns. It treats the main-body risks of a portfolio fairly accurately. We now need to take account of the fact that the model is not perfectly accurate. In particular, very large-magnitude returns occur much more frequently than the standard return model predicts, leading to far greater tail risk than the standard risk model acknowledges. The entire distribution of returns, not just the expected return and return volatility, is important to investors.

In this chapter, we look at the behavior of asset prices and alternative models to the joint normal model that might better explain return behavior. We will also see how market prices, especially of options, reflect these alternatives. In Chapter 13, we discuss stress tests, an approach to risk measurement that takes account of the prevalence of extreme returns. Tools such as VaR can help measure the risk of losses that, while large and unpleasant, will be a recurrent cost of doing business. The models described in this chapter and stress testing attempt to measure risks that are life-threatening to a financial firm.


We start by comparing the standard model, in which asset prices or risk factors are lognormally distributed, to actual market price behavior, as evidenced by the time-series behavior of their returns. ...

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