ANALYTICAL COMPARISONS OF OPTION PRICES IN STOCHASTIC VOLATILITY MODELS

Vicky Henderson

Mathematical Finance, 2005, vol. 15, issue 1, 49-59

Abstract: This paper gives an ordering on option prices under various well‐known martingale measures in an incomplete stochastic volatility model. Our central result is a comparison theorem that proves convex option prices are decreasing in the market price of volatility risk, the parameter governing the choice of pricing measure. The theorem is applied to order option prices under q‐optimal pricing measures. In doing so, we correct orderings demonstrated numerically in Heath, Platen, and Schweizer (Mathematical Finance, 11(4), 2001) in the special case of the Heston model.

Date: 2005
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