INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

Zhenyu Cui, J. Lars Kirkby (), Guanghua Lian and Duy Nguyen ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 08, 1-32

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.

Keywords: Stochastic volatility; exact probability densities; implied volatility; timer option (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024917500558

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