Affine Versus Non-Affine Stochastic Volatility and the Impact on Asset Allocation

Abstract

This paper analyzes the influence of affine versus non-affine stochastic volatility specifications on simulated distributions, option pricing, and asset allocation. We look at models that include stochastic volatility and jumps in the stock price and in its volatility. For the asset allocation problem we consider a CRRA investor who has access to one additional derivative, besides the stock and the money market account, and is restricted to a buy-and-hold strategy. We show that the assumption on the volatility structure has a very strong impact on simulated volatility distributions. Differences among these translate into the simulated stock price distributions, option prices, and the optimal portfolio positions. We are especially interested in the mistake the investor makes by choosing the convenient Heston (1993) specification over a (by assumption correct) non-affine volatility specification. We find that this leads to large utility losses for the investor, which are especially severe in models that do not include jumps. However, the investor can in most cases minimize his losses by including jumps to the affine volatility specification and by choosing the correct moneyness. He therefore can continue to use the convenient and numerically more easily accessible affine specification.