Financial options and statistical prediction intervals

Abstract

The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conclusions into prices for options and similar financial instruments. A prime feature of our results is that one can construct the trading strategy as if the prediction set had a 100 % probability. If, in fact, the set has probability $1-\alpha$, the hedging strategy will work with at least the same probability. Different types of prediction regions are considered. The starting value $\A$ for the trading strategy corresponding to the $1-\alpha$ prediction region is a form of long term value at risk. At the same time, $\A$ is coherent.