Analytical Comparisons of Option prices in Stochastic
Volatility Models
Vicky Henderson
Abstract
This paper orders option prices under various well known
martingale measures in an incomplete stochastic volatility model. The
central result is a comparison theorem which 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 the minimal martingale, q-optimal and minimal entropy measures. This
ordering depends on the mean variance tradeoff process whilst the specifics
of the volatility dynamics are not important. We illustrate our results by
analyzing the Hull and White, Heston and Stein and Stein models.
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