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A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation

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  • Vicky Henderson
  • David Hobson
  • Sam Howison
  • Tino Kluge

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. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. As a concrete example, we specialise to a variant of the Heston model. For this example we are able to deduce that option prices are decreasing in the parameter q.

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  • 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.
    • Handle: RePEc:sbs:wpsefe:2003mf02
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2003mf02.pdf
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    References listed on IDEAS

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    Cited by:

    1. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    2. 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.
    3. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.
    4. Joao Amaro de Matos & Ana Lacerda, 2006. "Equilibrium bid-ask spread of European derivatives in dry markets," Nova SBE Working Paper Series wp480, Universidade Nova de Lisboa, Nova School of Business and Economics.

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