Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification
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 formul...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/623945 |
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| author | Jixiang Xu Yanhua Tan Jinggui Gao Enmin Feng |
| author_facet | Jixiang Xu Yanhua Tan Jinggui Gao Enmin Feng |
| author_sort | Jixiang Xu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-df0a2380e40f43b9a43331a58c27c650 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-df0a2380e40f43b9a43331a58c27c6502025-08-20T02:21:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/623945623945Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter IdentificationJixiang Xu0Yanhua Tan1Jinggui Gao2Enmin Feng3School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, ChinaSchool of Sciences, Hebei University of Technology, Tianjin 300130, ChinaCollege of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266510, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, ChinaWe 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.http://dx.doi.org/10.1155/2013/623945 |
| spellingShingle | Jixiang Xu Yanhua Tan Jinggui Gao Enmin Feng Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification Journal of Applied Mathematics |
| title | Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification |
| title_full | Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification |
| title_fullStr | Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification |
| title_full_unstemmed | Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification |
| title_short | Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification |
| title_sort | pricing currency option based on the extension principle and defuzzification via weighting parameter identification |
| url | http://dx.doi.org/10.1155/2013/623945 |
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