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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/875319 |
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| _version_ | 1849408778017964032 |
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| author | Xiandong Wang Jianmin He Shouwei Li |
| author_facet | Xiandong Wang Jianmin He Shouwei Li |
| author_sort | Xiandong Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-75d247dda4b842ae8061d727f195fa1c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-75d247dda4b842ae8061d727f195fa1c2025-08-20T03:35:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/875319875319Compound Option Pricing under Fuzzy EnvironmentXiandong Wang0Jianmin He1Shouwei Li2School of Sciences, Changzhou Institute of Technology, Changzhou, Jiangsu 213002, ChinaSchool of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, ChinaSchool of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, ChinaConsidering 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.http://dx.doi.org/10.1155/2014/875319 |
| spellingShingle | Xiandong Wang Jianmin He Shouwei Li Compound Option Pricing under Fuzzy Environment Journal of Applied Mathematics |
| title | Compound Option Pricing under Fuzzy Environment |
| title_full | Compound Option Pricing under Fuzzy Environment |
| title_fullStr | Compound Option Pricing under Fuzzy Environment |
| title_full_unstemmed | Compound Option Pricing under Fuzzy Environment |
| title_short | Compound Option Pricing under Fuzzy Environment |
| title_sort | compound option pricing under fuzzy environment |
| url | http://dx.doi.org/10.1155/2014/875319 |
| work_keys_str_mv | AT xiandongwang compoundoptionpricingunderfuzzyenvironment AT jianminhe compoundoptionpricingunderfuzzyenvironment AT shouweili compoundoptionpricingunderfuzzyenvironment |