A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation

Abstract

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk. As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. As a concrete example, we specialise to a variant of the Heston model. For this example we are able to deduce that option prices are decreasing in the parameter q.