Compound Option Pricing under Fuzzy Environment

Compound Option Pricing under Fuzzy Environment

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 Gesk...

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Bibliographic Details
Published in:Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 821 - 829-876
Main Authors: Wang, Xiandong, He, Jianmin, Li, Shouwei
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Limiteds 01-01-2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Subjects:
Crisps
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Mathematical models
Options trading
Pricing
Pricing policies
Stochastic models
Volatility
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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 α, the α-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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/875319