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The α-hypergeometric stochastic volatility model

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  • Da Fonseca, José
  • Martini, Claude

Abstract

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of affine models, we define a new specification for the dynamics of the volatility. Within this framework we develop all the key elements to perform the pricing of vanilla European options as well as of volatility derivatives. We clarify the conditions under which the stock price is a martingale and illustrate how the model can be implemented.

Suggested Citation

  • Da Fonseca, José & Martini, Claude, 2016. "The α-hypergeometric stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1472-1502.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:5:p:1472-1502
    DOI: 10.1016/j.spa.2015.11.010
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    References listed on IDEAS

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    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    3. Andrey Itkin, 2013. "New solvable stochastic volatility models for pricing volatility derivatives," Review of Derivatives Research, Springer, vol. 16(2), pages 111-134, July.
    4. José da Fonseca & Martino Grasselli, 2011. "Riding on the smiles," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1609-1632.
    5. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 267-284, September.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. 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.
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    Citations

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    Cited by:

    1. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    2. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    3. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    4. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    5. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    6. Lo, C.C. & Nguyen, D. & Skindilias, K., 2017. "A Unified Tree approach for options pricing under stochastic volatility models," Finance Research Letters, Elsevier, vol. 20(C), pages 260-268.
    7. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    8. Ma, Jingtang & Yang, Wensheng & Cui, Zhenyu, 2021. "CTMC integral equation method for American options under stochastic local volatility models," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).

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