Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing
The aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options pricing. Firstly, the governing free-boundary PDEs are modified as a unified form of PDEs on the fixed space region; then...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/1838521 |
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| author | Yong Chen Jianjun Ma |
| author_facet | Yong Chen Jianjun Ma |
| author_sort | Yong Chen |
| collection | DOAJ |
| description | The aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options pricing. Firstly, the governing free-boundary PDEs are modified as a unified form of PDEs on the fixed space region; then performing Laplace-Carson transform (LCT) leads to ordinary differential equations (ODEs) which involve the unknown inverse functions of free boundaries. Secondly, the inverse free-boundary functions are approximated and optimized by solving of the free-boundary values of the perpetual American volatility options. Finally, the ODEs are solved by the finite difference methods (FDMs), and the results are restored via the numerical Laplace inversion. Numerical results confirm that the NCIMs outperform the FDMs for solving free-boundary PDEs in regard to the accuracy and computational time. |
| format | Article |
| id | doaj-art-998a77443b444fee9b34398edb5cede0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-998a77443b444fee9b34398edb5cede02025-02-03T06:12:27ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/18385211838521Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options PricingYong Chen0Jianjun Ma1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, ChinaInternational Business School, Sichuan International Studies University, Chongqing, 400031, ChinaThe aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options pricing. Firstly, the governing free-boundary PDEs are modified as a unified form of PDEs on the fixed space region; then performing Laplace-Carson transform (LCT) leads to ordinary differential equations (ODEs) which involve the unknown inverse functions of free boundaries. Secondly, the inverse free-boundary functions are approximated and optimized by solving of the free-boundary values of the perpetual American volatility options. Finally, the ODEs are solved by the finite difference methods (FDMs), and the results are restored via the numerical Laplace inversion. Numerical results confirm that the NCIMs outperform the FDMs for solving free-boundary PDEs in regard to the accuracy and computational time.http://dx.doi.org/10.1155/2018/1838521 |
| spellingShingle | Yong Chen Jianjun Ma Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing Discrete Dynamics in Nature and Society |
| title | Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing |
| title_full | Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing |
| title_fullStr | Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing |
| title_full_unstemmed | Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing |
| title_short | Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing |
| title_sort | numerical contour integral methods for free boundary partial differential equations arising in american volatility options pricing |
| url | http://dx.doi.org/10.1155/2018/1838521 |
| work_keys_str_mv | AT yongchen numericalcontourintegralmethodsforfreeboundarypartialdifferentialequationsarisinginamericanvolatilityoptionspricing AT jianjunma numericalcontourintegralmethodsforfreeboundarypartialdifferentialequationsarisinginamericanvolatilityoptionspricing |