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.
Publié le : 1991-08-14
Classification:
Diffusion approximation,
stochastic delay equations,
option pricing,
Black and Scholes formula,
60F17,
90A09
@article{1177005873,
author = {Kind, Paolo and Liptser, Robert Sh. and Runggaldier, Wolfgang J.},
title = {Diffusion Approximation in Past Dependent Models and Applications to Option Pricing},
journal = {Ann. Appl. Probab.},
volume = {1},
number = {4},
year = {1991},
pages = { 379-405},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005873}
}
Kind, Paolo; Liptser, Robert Sh.; Runggaldier, Wolfgang J. Diffusion Approximation in Past Dependent Models and Applications to Option Pricing. Ann. Appl. Probab., Tome 1 (1991) no. 4, pp. 379-405. http://gdmltest.u-ga.fr/item/1177005873/