Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity
Firstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman-Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset pri...
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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/10.1155/2013/875606 |
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| _version_ | 1832567127242964992 |
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| author | Jiexiang Huang Wenli Zhu Xinfeng Ruan |
| author_facet | Jiexiang Huang Wenli Zhu Xinfeng Ruan |
| author_sort | Jiexiang Huang |
| collection | DOAJ |
| description | Firstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman-Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset price, which exists an affine solution. Then, we employ the fast Fourier Transform (FFT) method to obtain the approximate numerical solution of a power option which is conveniently designed with different risks or prices. Finally, we find the FFT method to compute that our option price has better stability, higher accuracy, and faster speed, compared to Monte Carlo approach. |
| format | Article |
| id | doaj-art-be6a8e74664b400989977b91ced47bb5 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-be6a8e74664b400989977b91ced47bb52025-02-03T01:02:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/875606875606Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump IntensityJiexiang Huang0Wenli Zhu1Xinfeng Ruan2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaSchool of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaSchool of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaFirstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman-Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset price, which exists an affine solution. Then, we employ the fast Fourier Transform (FFT) method to obtain the approximate numerical solution of a power option which is conveniently designed with different risks or prices. Finally, we find the FFT method to compute that our option price has better stability, higher accuracy, and faster speed, compared to Monte Carlo approach.http://dx.doi.org/10.1155/2013/875606 |
| spellingShingle | Jiexiang Huang Wenli Zhu Xinfeng Ruan Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity Journal of Applied Mathematics |
| title | Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity |
| title_full | Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity |
| title_fullStr | Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity |
| title_full_unstemmed | Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity |
| title_short | Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity |
| title_sort | fast fourier transform based power option pricing with stochastic interest rate volatility and jump intensity |
| url | http://dx.doi.org/10.1155/2013/875606 |
| work_keys_str_mv | AT jiexianghuang fastfouriertransformbasedpoweroptionpricingwithstochasticinterestratevolatilityandjumpintensity AT wenlizhu fastfouriertransformbasedpoweroptionpricingwithstochasticinterestratevolatilityandjumpintensity AT xinfengruan fastfouriertransformbasedpoweroptionpricingwithstochasticinterestratevolatilityandjumpintensity |