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A new analytical approximation for European puts with stochastic volatility

Journal Article


Abstract


  • In this paper, we apply singular perturbation techniques to price European puts with a stochastic volatility model, and derive a simple and elegant analytical formula as an approximation for the value of European put options. In contrast to the existing Heston’s semi-analytical formula, this approximation has the following unique feature: the latter only involves the standard normal distribution function, which is as fast and easy to implement as the Black–Scholes formula; whereas the former requires the evaluation of a logarithm with a complex argument during the involved Fourier inverse transform, which may sometimes result in numerical instability. Various numerical experiments suggest that our new formula can achieve a high order of accuracy for a large class of option derivatives with relatively short tenor.

Publication Date


  • 2010

Citation


  • Zhu, S. & Chen, W. (2010). A new analytical approximation for European puts with stochastic volatility. Applied Mathematics Letters, 23 (6), 687-692.

Scopus Eid


  • 2-s2.0-77950188377

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3311

Has Global Citation Frequency


Number Of Pages


  • 5

Start Page


  • 687

End Page


  • 692

Volume


  • 23

Issue


  • 6

Abstract


  • In this paper, we apply singular perturbation techniques to price European puts with a stochastic volatility model, and derive a simple and elegant analytical formula as an approximation for the value of European put options. In contrast to the existing Heston’s semi-analytical formula, this approximation has the following unique feature: the latter only involves the standard normal distribution function, which is as fast and easy to implement as the Black–Scholes formula; whereas the former requires the evaluation of a logarithm with a complex argument during the involved Fourier inverse transform, which may sometimes result in numerical instability. Various numerical experiments suggest that our new formula can achieve a high order of accuracy for a large class of option derivatives with relatively short tenor.

Publication Date


  • 2010

Citation


  • Zhu, S. & Chen, W. (2010). A new analytical approximation for European puts with stochastic volatility. Applied Mathematics Letters, 23 (6), 687-692.

Scopus Eid


  • 2-s2.0-77950188377

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3311

Has Global Citation Frequency


Number Of Pages


  • 5

Start Page


  • 687

End Page


  • 692

Volume


  • 23

Issue


  • 6