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August, 1991 Diffusion Approximation in Past Dependent Models and Applications to Option Pricing
Paolo Kind, Robert Sh. Liptser, Wolfgang J. Runggaldier
Ann. Appl. Probab. 1(3): 379-405 (August, 1991). DOI: 10.1214/aoap/1177005873

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.

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Paolo Kind. Robert Sh. Liptser. Wolfgang J. Runggaldier. "Diffusion Approximation in Past Dependent Models and Applications to Option Pricing." Ann. Appl. Probab. 1 (3) 379 - 405, August, 1991. https://doi.org/10.1214/aoap/1177005873

Information

Published: August, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0734.60035
MathSciNet: MR1111524
Digital Object Identifier: 10.1214/aoap/1177005873

Subjects:
Primary: 60F17
Secondary: 90A09

Keywords: Black and Scholes formula , diffusion approximation , option pricing , stochastic delay equations

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.1 • No. 3 • August, 1991
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