Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market
We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/236091 |
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| _version_ | 1832562952641708032 |
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| author | Shuang Li Yanli Zhou Xinfeng Ruan B. Wiwatanapataphee |
| author_facet | Shuang Li Yanli Zhou Xinfeng Ruan B. Wiwatanapataphee |
| author_sort | Shuang Li |
| collection | DOAJ |
| description | We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options. |
| format | Article |
| id | doaj-art-6cf2f8ee18ec4d7b9e24186278810b98 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6cf2f8ee18ec4d7b9e24186278810b982025-02-03T01:21:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/236091236091Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete MarketShuang Li0Yanli Zhou1Xinfeng Ruan2B. Wiwatanapataphee3Department of Maths and Statistics, Curtin University, Perth, WA 6845, AustraliaDepartment of Maths and Statistics, Curtin University, Perth, WA 6845, AustraliaSchool of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaDepartment of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandWe study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.http://dx.doi.org/10.1155/2014/236091 |
| spellingShingle | Shuang Li Yanli Zhou Xinfeng Ruan B. Wiwatanapataphee Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market Abstract and Applied Analysis |
| title | Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market |
| title_full | Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market |
| title_fullStr | Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market |
| title_full_unstemmed | Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market |
| title_short | Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market |
| title_sort | pricing of american put option under a jump diffusion process with stochastic volatility in an incomplete market |
| url | http://dx.doi.org/10.1155/2014/236091 |
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