Linear stochastic volatility models
AbstractIn this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and Heston stochastic volatility model. For a linear stochastic volatility model we derive representations for the probability density function of the arbitrage price of a financial asset and the prices of European call and put options. A closed-form formulae for the density function and the prices of European call and put options are given for log-normal stochastic volatility model. We also obtain present some new results for Heston and extended Heston stochastic volatility models.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0909.4765.
Date of creation: Sep 2009
Date of revision: May 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-10-03 (All new papers)
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- Marc Romano & Nizar Touzi, 1997. "Contingent Claims and Market Completeness in a Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(4), pages 399-412.
- Y. Maghsoodi, 2007. "Exact Solution Of A Martingale Stochastic Volatility Option Problem And Its Empirical Evaluation," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 17(2), pages 249-265.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
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