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Analytical Comparisons of Option prices in Stochastic Volatility Models

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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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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf03.

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Date of creation: 2002
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Handle: RePEc:sbs:wpsefe:2002mf03

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52. [Downloadable!] (restricted)
  2. Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany. [Downloadable!]
  3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  4. Michael Belledin & Christian Schlag, 1999. "An Empirical Comparison of Alternative Stochastic Volatility Models," Working Paper Series: Finance and Accounting 38, Department of Finance, Goethe University Frankfurt am Main. [Downloadable!]
  5. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Blackwell Publishing, vol. 11(4), pages 385-413. [Downloadable!] (restricted)
  6. HuyËn Pham & Jean Paul Laurent, 1999. "Dynamic programming and mean-variance hedging," Finance and Stochastics, Springer, vol. 3(1), pages 83-110. [Downloadable!] (restricted)
  7. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March. [Downloadable!] (restricted)
  8. Gourieroux, Christian & Laurent, Jean-Paul & Pham, Huyên, 1996. "Mean-variance hedging and numeraire," CEPREMAP Working Papers (Couverture Orange) 9611, CEPREMAP.
  9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  10. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198. [Downloadable!] (restricted)
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  1. Thierry Chauveau & Hayette Gatfaoui, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Research Paper Series 122, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  2. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series 2003mf02, Oxford Financial Research Centre. [Downloadable!]
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