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Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options

Author

Listed:
  • ZHENYU CUI

    (School of Business, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07310, USA)

  • J. LARS KIRKBY

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30318, USA)

  • GUANGHUA LIAN

    (Haas School of Business, University of California, Berkeley, California, USA4School of Commerce, University of South Australia, Adelaide, Austrailia)

  • DUY NGUYEN

    (Department of Mathematics, Marist College, 3399 North Road, Poughkeepsie, NY 12601, USA)

Abstract

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, 3/2, and a special case of the α-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The α-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the 3/2 model and a special case of the α-Hypergeometric model.

Suggested Citation

  • Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:08:n:s0219024917500558
    DOI: 10.1142/S0219024917500558
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.

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