Beyond Implied Volatility: Estimating Robust Risk-Return Probability Distributions

We have observed in studying financial markets that 100-year floods occur quite often, maybe several every decade, so we know simple risk models can be inadequate and misleading. Many financial risk models start with a risk reading taken from the options markets — implied volatility. Implied volatility is a standard deviation based metric and, while not required, users typically embed the presumption of a bell-shaped curve. Starting with implied volatility, the risk manager or financial analyst then must work to augment the tails of the probability distribution to increase the odds of extreme events actually happening to align more closely with historical experience. After all, it is the extreme events that can do the most financial damage, so it is critical that the expected probability distribution be augmented beyond a simple standard deviation analysis to properly account for the possibilities…