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Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression
When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the...
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| Published in: | Journal of the Korean Statistical Society 2011, 40(2), , pp.227-238 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c444t-c3f21c0771a266735316f5257b4820b50dd7752a217b1e84e20c86b9b7decf8e3 |
| container_end_page | 238 |
| container_issue | 2 |
| container_start_page | 227 |
| container_title | Journal of the Korean Statistical Society |
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| creator | Song, Seongjoo Jeong, Jaehong Song, Jongwoo |
| description | When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black–Scholes price assuming that the price process converges weakly to the Black–Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. The proposed price explains the market option data better than the Black–Scholes price in real data application with KOSPI 200. |
| doi_str_mv | 10.1016/j.jkss.2010.10.001 |
| format | article |
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This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black–Scholes price assuming that the price process converges weakly to the Black–Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. 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Korean Stat. Soc</addtitle><description>When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black–Scholes price assuming that the price process converges weakly to the Black–Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. The proposed price explains the market option data better than the Black–Scholes price in real data application with KOSPI 200.</description><subject>Applied Statistics</subject><subject>Asymptotic expansion</subject><subject>Bayesian Inference</subject><subject>Lévy process</subject><subject>Nonlinear regression</subject><subject>Option pricing</subject><subject>Statistical Theory and Methods</subject><subject>Statistics</subject><subject>Statistics and Computing/Statistics Programs</subject><subject>통계학</subject><issn>1226-3192</issn><issn>2005-2863</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE1qwzAUhEVpoWnaC3SlbRd2JdmWHOgmhP4EAoWQroUtPxs5iWQkO5Aj9Ry9WOW666wezJtvYAahR0piSih_buN2733MyJ8QE0Kv0IwRkkUs58k1mlHGeJTQBbtFd963hPCUMjJD26U_H7ve9lph2_XaGtw5rbRp8GAqcLgbHETtcOzw5uf7dA5fq8B78PikC2ysOWgDhcMOGhf0EHCPburi4OHh_87R19vrbvURbT7f16vlJlJpmvaRSmpGFRGCFoxzkWQJ5XXGMlGmOSNlRqpKiIwVjIqSQp4CIyrn5aIUFag6h2SOnqZc42q5V1raQv_dxsq9k8vtbi0pWWQ0T4OXTV7lrPcOahlaHgt3Dg45LihbOS4oxwVHLSwYoGSCfDCbBpxs7eBM6HSZepkoCN1POlBeaTAKKu1A9bKy-hL-C9Lmi94</recordid><startdate>20110601</startdate><enddate>20110601</enddate><creator>Song, Seongjoo</creator><creator>Jeong, Jaehong</creator><creator>Song, Jongwoo</creator><general>Elsevier B.V</general><general>Springer Singapore</general><general>한국통계학회</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ACYCR</scope></search><sort><creationdate>20110601</creationdate><title>Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression</title><author>Song, Seongjoo ; Jeong, Jaehong ; Song, Jongwoo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c444t-c3f21c0771a266735316f5257b4820b50dd7752a217b1e84e20c86b9b7decf8e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Applied Statistics</topic><topic>Asymptotic expansion</topic><topic>Bayesian Inference</topic><topic>Lévy process</topic><topic>Nonlinear regression</topic><topic>Option pricing</topic><topic>Statistical Theory and Methods</topic><topic>Statistics</topic><topic>Statistics and Computing/Statistics Programs</topic><topic>통계학</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Song, Seongjoo</creatorcontrib><creatorcontrib>Jeong, Jaehong</creatorcontrib><creatorcontrib>Song, Jongwoo</creatorcontrib><collection>CrossRef</collection><collection>Korean Citation Index</collection><jtitle>Journal of the Korean Statistical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Song, Seongjoo</au><au>Jeong, Jaehong</au><au>Song, Jongwoo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression</atitle><jtitle>Journal of the Korean Statistical Society</jtitle><stitle>J. 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| identifier | ISSN: 1226-3192 |
| ispartof | Journal of the Korean Statistical Society, 2011, 40(2), , pp.227-238 |
| issn | 1226-3192 2005-2863 |
| language | eng |
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| source | Springer Link |
| subjects | Applied Statistics Asymptotic expansion Bayesian Inference Lévy process Nonlinear regression Option pricing Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs 통계학 |
| title | Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression |
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