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Convergence to Black-Scholes for ergodic volatility models

Published online by Cambridge University Press:  07 September 2005

JOSEPH G. CONLON  and
MICHAEL G. SULLIVAN
JOSEPH G. CONLON
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA email: [email protected]
MICHAEL G. SULLIVAN
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, MA 01003-9305, USA email: [email protected]
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Abstract

We study the effect of stochastic volatility on option prices. In the fast mean-reversion model for stochastic volatility of [5], we show that there is a full asymptotic expansion for the option price, centered at the Black-Scholes price. We show how to callibrate the first two terms in the expansion with the implied volatility surface. We show, however, that this price does not converge in a strong sense to Black-Scholes as the mean-reversion rate increases.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 16 , Issue 3 , June 2005 , pp. 385 - 409
Copyright
2005 Cambridge University Press

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