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Asymptotic analysis for stochastic volatility: Edgeworth expansion

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  • Masaaki Fukasawa

Abstract

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model.

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  • Masaaki Fukasawa, 2010. "Asymptotic analysis for stochastic volatility: Edgeworth expansion," Papers 1004.2106, arXiv.org.
  • Handle: RePEc:arx:papers:1004.2106
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    File URL: http://arxiv.org/pdf/1004.2106
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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Fitzsimmons, P. J. & Pitman, Jim, 1999. "Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 117-134, January.
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