The Mathematical Institute, University of Oxford, Eprints Archive

A comparison of option prices under different pricing measures in a stochastic volatility model with correlation

Henderson, Vicky and Hobson, David and Howison, Sam and Kluge, Tino (2003) A comparison of option prices under different pricing measures in a stochastic volatility model with correlation. Review of Derivatives Research . (In Press)

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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. The $q$-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.

As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter $q$. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying $q$.

Item Type:Article
Uncontrolled Keywords:Option pricing, derivative pricing, stochastic volatility
Subjects:D - G > Game theory, mathematical finance, economics, social and behavioral sciences
Research Groups:Mathematical and Computational Finance Group
ID Code:134
Deposited By:Sam Howison
Deposited On:08 Oct 2004
Last Modified:20 Jul 2009 14:18

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