Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T18:15:22.997Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)