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Analytical Comparisons Of Option Prices In Stochastic Volatility Models

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  • Vicky Henderson

Abstract

This paper gives an ordering on option prices under various well‐known martingale measures in an incomplete stochastic volatility model. Our central result is a comparison theorem that 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 q‐optimal pricing measures. In doing so, we correct orderings demonstrated numerically in Heath, Platen, and Schweizer (Mathematical Finance, 11(4), 2001) in the special case of the Heston model.

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  • Vicky Henderson, 2005. "Analytical Comparisons Of Option Prices In Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 49-59, January.
    • Handle: RePEc:bla:mathfi:v:15:y:2005:i:1:p:49-59
    DOI: 10.1111/j.0960-1627.2005.00210.x
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    Cited by:

    1. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    2. Arun Chockalingam & Kumar Muthuraman, 2011. "American Options Under Stochastic Volatility," Operations Research, INFORMS, vol. 59(4), pages 793-809, August.
    3. Maciej Augustyniak & Frédéric Godin & Clarence Simard, 2017. "Assessing the effectiveness of local and global quadratic hedging under GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1305-1318, September.
    4. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    5. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    6. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    7. David Hobson, 2010. "Comparison results for stochastic volatility models via coupling," Finance and Stochastics, Springer, vol. 14(1), pages 129-152, January.
    8. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    9. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    10. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2005. "A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation," Review of Derivatives Research, Springer, vol. 8(1), pages 5-25, June.
    11. George M. Mukupa & Elias R. Offen, 2020. "The Semimartingale Equilibrium Risk Premium for a Risk Seeking Investor," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-13, August.
    12. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.

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