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 optimal pricing measures. The 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 varianceoptimal 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 HullWhite 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 . Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying .
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:  29 May 2015 18:17 
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