TITLE:
Recent Developments in Fuzzy Sets Approach in Option Pricing
AUTHORS:
Srimantoorao S. Appadoo, Aerambamoorthy Thavaneswaran
KEYWORDS:
Membership Function; Fuzzy Coefficient; Black-Scholes Partial Differential Equations (PDE); Asset-or-Nothing Option; Fuzzy Real Options
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.2,
May
24,
2013
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.