Asymptotic analysis for stochastic volatility: Edgeworth expansion
作者： Masaaki Fukasawa
DOI:
关键词: Ergodic theory 、 Bounded function 、 Applied mathematics 、 Singular perturbation 、 Mathematics 、 Edgeworth series 、 Stochastic volatility 、 Stochastic game 、 Asymptotic analysis 、 Asymptotic expansion
摘要: The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light Edgeworth expansion ergodic diffusions. asymptotic around Black-Scholes price and uniform bounded payoff func- tions. result provides validation existing singular perturbation fast mean reverting model.
arxiv.org
harvard.edu参考文章(11)
Jim Gatheral, The Volatility Surface: A Practitioner's Guide ,(2006)
Anatoliĭ Vladimirovich Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations ,(2008)
Rabi N. Bhattacharya, R. Ranga Rao, Normal Approximation and Asymptotic Expansions ,(1976)
J. P. Fouque, G. Papanicolaou, R. Sircar, K. Solna, Singular Perturbations in Option Pricing Siam Journal on Applied Mathematics. ,vol. 63, pp. 1648- 1665 ,(2003) , 10.1137/S0036139902401550
Rafail Z. Khasminskii, G. Yin, Uniform Asymptotic Expansions for Pricing European Options Applied Mathematics and Optimization. ,vol. 52, pp. 279- 296 ,(2005) , 10.1007/S00245-005-0833-2
I. S. Borisov, Estimate of the rate of convergence of distributions of additive functionals of a sequence of sums of independent random variables Siberian Mathematical Journal. ,vol. 19, pp. 371- 383 ,(1978) , 10.1007/BF01875286
Valentin V. Petrov, Sums of Independent Random Variables ,(1975)
Nakahiro Yoshida, Malliavin calculus and asymptotic expansion for martingales Probability Theory and Related Fields. ,vol. 109, pp. 301- 342 ,(1997) , 10.1007/S004400050134
Masaaki Fukasawa, Asymptotic analysis for stochastic volatility: martingale expansion Finance and Stochastics. ,vol. 15, pp. 635- 654 ,(2011) , 10.1007/S00780-010-0136-6
Peter Hall, The Bootstrap and Edgeworth Expansion ,(1992)