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Nonlinear PDE approach for option pricing with stochastic volatility by using fuzzy sets theory.

Author(s)
Hua Lia Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, China
Anthony Wareb Department of Mathematics and Statistics University of Calgary, Calgary T2N1N4, Alberta, Canada
Anatoliy Swishchukb Department of Mathematics and Statistics University of Calgary, Calgary T2N1N4, Alberta, Canada
Abstract
This paper is to price European options for assets with stochastic volatility in using fuzzy set theory. The main idea is to transform the probability distribution of stochastic volatility to its possibility distribution (from `volatility smile to volatility frown ) and reduce the problem to a fuzzy stochastic process for underlying asset with volatility as a fuzzy number associated with initial stochastic volatility. We\ then price the corresponding European options by introducing the non-linear fuzzy PDE approach.
Publication Details
Page(s) 508-514
DOI DOI not available
Published Journal: Journal of Theoretical and Applied Information Technology, Volume: 45, Issue: 2, Year: 2012

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