Compound option pricing under fuzzy environment. (English) Zbl 1406.91457

Wang, Xiandong; He, Jianmin; Li, Shouwei

J. Appl. Math. 2014, Article ID 875319, 9 p. (2014).

Summary: Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each \(\alpha\), the \(\alpha\)-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
91G10	Portfolio theory
91G80	Financial applications of other theories
03E72	Theory of fuzzy sets, etc.