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Recent Developments in Fuzzy Sets Approach in Option Pricing
Department of Supply Chain Management, University of Manitoba, Winnipeg, Canada
Department of Statistics, University of Manitoba, Winnipeg, Canada
- 1 Department of Supply Chain Management, University of Manitoba, Winnipeg, Canada
- 2 Department of Statistics, University of Manitoba, Winnipeg, Canada
Journal of Mathematical Finance·Volume 03 (2013)·Pages 312–322·Published 24 May 2013·DOI10.4236/jmf.2013.32031
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Abstract
Recently there has been growing interest in fuzzy option pricing. Carlsson and Fuller [1] were the first to study the fuzzy real options and Thavaneswaran et al. [2] demonstrated the superiority of the fuzzy forecasts and then derived the membership function for the European call price by fuzzifying the interest rate, volatility and the initial value of the stock price. In this paper, we discuss recent developments in fuzzy option pricing based on Black - Scholes models. Fuzzy coefficient Black - Scholes partial differential equations (PDE) are derived. Membership function of the call price is given. The asset-or-nothing option by fuzzifying the maturity value of the stock price using adaptive fuzzy numbers is also discussed in some detail.
KeywordsMembership FunctionFuzzy CoefficientBlack-Scholes Partial Differential Equations (PDE)Asset-or-Nothing OptionFuzzy Real Options
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