Question:

In the FRM, we are repeatedly reminded that asset returns are likely to exhibit “fat-tails” (kurtosis > 3. In addition to being skewed and unstable).

If fat-tails are true, it is dangerous to depend on the normal distribution to model returns (see Taleb’s Black Swan). Several remedies (or solutions or supplements) are suggested in the cirriculum. Cite a few solutions to the problem that, as Linda Allen writes, “normality cannot be salvaged?”

Answer:

We can think about the three primary value at risk (VaR) approaches: parametric, historical and Monte Carlo simulation. (the others are hybrids or variations).

* Historical simulation requires no distributional assumption. It is not burdened by normal tails
* Monte Carlo simulation is flexible in the algorithm. It is not necessarily burdened by normal tails.
* While we typically/often refer to the specific parametric VaR that Jorion calls delta normal, and this is the focus of much review due to classical theory, other distributions can be employed.

Both of Wilmott’s simulations are well-suited to modeling non-normal returns:

* Monte Carlo simulation (his example, GMB, assumes normal returns/lognormal levels, but any algorithm can be specified)
* Bootstrapping: this approach has no distributional assumption

Also, Wilmott introduced extreme value theory (EVT):

* By definition, extreme value theory (EVT) is meant to address the estimation of (non-normal) tail risk

Allen reviews at least three approaches that do not depend on normality:

* Historical simulation
* The hybrid approach (combines historical simulation and EWMA)
* MDE