INTEGRAL REPRESENTATION of PROBABILITY DENSITY of STOCHASTIC VOLATILITY MODELS and TIMER OPTIONS

Zhenyu Cui, J. Lars Kirkby, Guanghua Lian, Duy Nguyen

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.

Original languageEnglish
Article number1750055
JournalInternational Journal of Theoretical and Applied Finance
Volume20
Issue number8
DOIs
StatePublished - 1 Dec 2017

Keywords

  • Stochastic volatility
  • exact probability densities
  • implied volatility
  • timer option

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