Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification
Joint Authors
Feng, Enmin
Tan, Yanhua
Gao, Jinggui
Xu, Jixiang
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-14
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We present a fuzzy version of the Garman-Kohlhagen (FG-K) formula for pricing European currency option based on the extension principle.
In order to keep consistent with the real market, we assume that the interest rate, the spot exchange rate, and the volatility are fuzzy numbers in the FG-K formula.
The conditions of a basic proposition about the fuzzy-valued functions of fuzzy subsets are modified.
Based on the modified conditions and the extension principle, we prove that the fuzzy price obtained from the FG-K formula for European currency option is a fuzzy number.
To simplify the trade, the weighted possibilistic mean (WPM) value with a weighting function is adopted to defuzzify the fuzzy price to a crisp price.
The numerical example shows our method makes the α-level set of fuzzy price smaller, which decreases the fuzziness.
The example also indicates that the WPM value has different approximation effects to real market price by taking different values of weighting parameter in the weighting function.
Inspired by this example, we provide a method, which can identify the optimal parameter.
American Psychological Association (APA)
Xu, Jixiang& Tan, Yanhua& Gao, Jinggui& Feng, Enmin. 2013. Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-485994
Modern Language Association (MLA)
Xu, Jixiang…[et al.]. Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification. Journal of Applied Mathematics No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-485994
American Medical Association (AMA)
Xu, Jixiang& Tan, Yanhua& Gao, Jinggui& Feng, Enmin. Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-485994
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-485994