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Convergence to Black-Scholes for ergodic volatility models

  • JOSEPH G. CONLON (a1) and MICHAEL G. SULLIVAN (a2)

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.

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