Pricing formulas, model error and hedging derivative portfolios

Abstract

We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic variations in the individual assets described by the formula. The paper makes simple and natural assumptions for how these risks behave. These extra risks should always be included when using the formula as a basis for portfolio management. We investigate an idealized typical portfolio problem, and argue that a rational and workable trading strategy can be based on minimizing the quadratic risk over the time intervals between trades. The example of the variance gamma pricing formula for equity derivatives is explored, and the method is seen to yield tractable decision strategies in this case.