Diffusion Approximation in Past Dependent Models and Applications to Option Pricing

Authors
Kind, Paolo Liptser, Robert Sh. Runggaldier, Wolfgang J.
Citation
Kind, Paolo et al., Diffusion Approximation in Past Dependent Models and Applications to Option Pricing, Annals of applied probability , 1(3), 1991, pp. 379-405
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
1
Issue
3
Year of publication
1991
Pages
379 - 405
Database
ACNP
SICI code
Abstract
We obtain a diffusion approximation result for processes satisfying equations with past-dependent coefficients. We apply this result to a model of option pricing, in which the underlying asset price volatility depends on past evolution, and obtain a generalized (asymptotic) Black and Scholes formula.