Analytical binomial lookback options with double-exponential jumps
We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A modified binomial tree method for currency lookback options. Acta Mathematica Sinica, 16, 445–454; Kou, S., & Wang, H. (2004)....
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| Published in | Journal of the Korean Statistical Society Vol. 38; no. 4; pp. 397 - 404 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Elsevier B.V
01.12.2009
Springer Singapore 한국통계학회 |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1226-3192 2005-2863 |
| DOI | 10.1016/j.jkss.2009.07.002 |
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| Abstract | We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A modified binomial tree method for currency lookback options.
Acta Mathematica Sinica, 16, 445–454; Kou, S., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model.
Management Science, 50, 1178–1192] and [Park, H.S., Kim, K.I., & Qian, X. (2009). A Mathematical modeling for the Lookback option with jump diffusion using Binomial tree method.
Journal of Computational and Applied Mathematics, preprint], we show the equivalence between the adjusted binomial tree method and the explicit difference scheme. The convergence is also theoretically proved through the notion of viscosity solution. Numerical results coincide with the theoretical results. |
|---|---|
| AbstractList | We study the problem of the convergence of the adjusted binomial lookback option in
double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A
modified binomial tree method for currency lookback options. Acta Mathematica Sinica,
16, 445454; Kou, S., & Wang, H. (2004). Option pricing under a double exponential
jump diffusion model. Management Science, 50, 11781192] and [Park, H.S., Kim, K.I., &
Qian, X. (2009). A Mathematical modeling for the Lookback option with jump diffusion
using Binomial tree method. Journal of Computational and Applied Mathematics, preprint],
we show the equivalence between the adjusted binomial tree method and the explicit
difference scheme. The convergence is also theoretically proved through the notion of
viscosity solution. Numerical results coincide with the theoretical results. KCI Citation Count: 2 We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A modified binomial tree method for currency lookback options. Acta Mathematica Sinica, 16, 445–454; Kou, S., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192] and [Park, H.S., Kim, K.I., & Qian, X. (2009). A Mathematical modeling for the Lookback option with jump diffusion using Binomial tree method. Journal of Computational and Applied Mathematics, preprint], we show the equivalence between the adjusted binomial tree method and the explicit difference scheme. The convergence is also theoretically proved through the notion of viscosity solution. Numerical results coincide with the theoretical results. We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A modified binomial tree method for currency lookback options. Acta Mathematica Sinica , 16, 445–454; Kou, S., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science , 50, 1178–1192] and [Park, H.S., Kim, K.I., & Qian, X. (2009). A Mathematical modeling for the Lookback option with jump diffusion using Binomial tree method. Journal of Computational and Applied Mathematics , preprint], we show the equivalence between the adjusted binomial tree method and the explicit difference scheme. The convergence is also theoretically proved through the notion of viscosity solution. Numerical results coincide with the theoretical results. |
| Author | Park, Hyun Suk |
| Author_xml | – sequence: 1 givenname: Hyun Suk surname: Park fullname: Park, Hyun Suk email: hspark@postech.ac.kr organization: Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea |
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| Cites_doi | 10.1111/j.1540-6261.1993.tb05130.x 10.1016/0304-405X(79)90015-1 10.1287/mnsc.48.8.1086.166 10.1111/j.1467-9965.1996.tb00111.x 10.1287/mnsc.1030.0163 10.1007/s002459900042 10.1016/S0294-1449(16)30106-8 10.1007/s101140000068 10.1137/S0363012991223595 10.3233/ASY-1991-4305 10.1137/S0036142902414220 10.1137/S0036142902409744 10.1016/S0261-5606(96)00052-6 10.1016/0304-405X(76)90023-4 10.1007/s007800050060 10.3905/jod.1993.407869 10.1016/j.jmaa.2006.07.042 10.1016/S0377-0427(02)00903-2 10.1090/S0273-0979-1992-00266-5 10.2307/2329069 10.2307/2327238 |
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| Keywords | 65C20 60H30 Partial integro-differential equation Viscosity solution Exponential jumps Adjusted binomial tree method 62P05 91B28 Lookback option Stochastic differential equation |
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| References_xml | – volume: 7 start-page: 229 year: 1979 end-page: 264 ident: b7 article-title: Option pricing: A simplified approach publication-title: Journal of Financial Econometrics – volume: 6 start-page: 17 year: 1996 end-page: 51 ident: b5 article-title: Pricing of American Path-dependent Contingent Claims publication-title: Mathematical Finance – volume: 1 start-page: 21 year: 1993 end-page: 31 ident: b11 article-title: Efficient procedures for valuing European and American path-dependent options publication-title: Journal of Derivatives – volume: 48 start-page: 1086 year: 2002 end-page: 1101 ident: b14 article-title: A jump diffusion model for option pricing publication-title: Management Science – volume: 16 start-page: 173 year: 1997 end-page: 187 ident: b6 article-title: Currency lookback options and observation frequency: A binomial approach publication-title: Journal of International Money and Finance – volume: 13 start-page: 293 year: 1996 end-page: 317 ident: b1 article-title: Viscosity solution of nonlinear integro-differential equations publication-title: Annales de l’Institut Henri Poincaré Analyse Non Linéaire – volume: 16 start-page: 445 year: 2000 end-page: 454 ident: b9 article-title: A modified binomial tree method for currency lookback options publication-title: Acta Mathematica Sinica – volume: 42 start-page: 1094 year: 2004 end-page: 1109 ident: b12 article-title: Convergence of binomial tree method for European/American path-dependent options publication-title: SIAM Journal on Numerical Analysis – volume: 34 start-page: 1111 year: 1979 end-page: 1128 ident: b10 article-title: Path dependent options: Buy at the Low, Sell at the High publication-title: Journal of Finance – volume: 32 start-page: 612 year: 1994 end-page: 634 ident: b3 article-title: Optimal control of the L norm of a diffusion process publication-title: SIAM Journal on Control and Optimization – volume: 156 start-page: 23 year: 2003 end-page: 45 ident: b21 article-title: Numerical Analysis on binomial tree methods for a jump-diffusion model publication-title: Journal of Computational and Applied Mathematics – reference: Park, H. S., Kim, K. I., & Qian, X. (2009). 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article-title: Jump diffusion option valuation in discrete time publication-title: Journal of Finance doi: 10.1111/j.1540-6261.1993.tb05130.x – volume: 7 start-page: 229 year: 1979 end-page: 264 ident: CR7 article-title: Option pricing: A simplified approach publication-title: Journal of Financial Econometrics doi: 10.1016/0304-405X(79)90015-1 – volume: 48 start-page: 1086 year: 2002 end-page: 1101 ident: CR14 article-title: A jump diffusion model for option pricing publication-title: Management Science doi: 10.1287/mnsc.48.8.1086.166 – volume: 6 start-page: 17 year: 1996 end-page: 51 ident: CR5 article-title: Pricing of American Path-dependent Contingent Claims publication-title: Mathematical Finance doi: 10.1111/j.1467-9965.1996.tb00111.x – volume: 50 start-page: 1178 year: 2004 end-page: 1192 ident: CR15 article-title: Option pricing under a double exponential jump diffusion model publication-title: Management Science doi: 10.1287/mnsc.1030.0163 – volume: 35 start-page: 145 year: 1997 end-page: 164 ident: CR19 article-title: Optimal stopping, free boundary and American option in a jump-diffusion model publication-title: Applied Mathematics and Optimization doi: 10.1007/s002459900042 – volume: 13 start-page: 293 year: 1996 end-page: 317 ident: CR1 article-title: Viscosity solution of nonlinear integro-differential equations publication-title: Annales de l’Institut Henri Poincaré Analyse Non Linéaire doi: 10.1016/S0294-1449(16)30106-8 – volume: 16 start-page: 445 year: 2000 end-page: 454 ident: CR9 article-title: A modified binomial tree method for currency lookback options publication-title: Acta Mathematica Sinica doi: 10.1007/s101140000068 – volume: 32 start-page: 612 year: 1994 end-page: 634 ident: CR3 article-title: Optimal control of the L norm of a diffusion process publication-title: SIAM Journal on Control and Optimization doi: 10.1137/S0363012991223595 – volume: 1 start-page: 271 year: 1991 end-page: 283 ident: CR4 article-title: Convergence of approximation schemes for fully nonlinear second order equations publication-title: Asymptotic Analysis doi: 10.3233/ASY-1991-4305 – volume: 42 start-page: 1094 year: 2004 end-page: 1109 ident: CR12 article-title: Convergence of binomial tree method for European/American path-dependent options publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/S0036142902414220 – volume: 42 start-page: 1899 year: 2005 end-page: 1913 ident: CR20 article-title: Convergence of the binomial tree method for American options in a jump-diffusion model publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/S0036142902409744 – volume: 16 start-page: 173 year: 1997 end-page: 187 ident: CR6 article-title: Currency lookback options and observation frequency: A binomial approach publication-title: Journal of International Money and Finance doi: 10.1016/S0261-5606(96)00052-6 – year: 2009 ident: CR18 article-title: A mathematical modeling for the Lookback option with jump diffusion using Binomial tree method publication-title: Journal of Computational and Applied Mathematics – volume: 34 start-page: 1111 year: 1979 end-page: 1128 ident: CR10 article-title: Path dependent options: Buy at the Low, Sell at the High publication-title: Journal of Finance – volume: 3 start-page: 145 year: 1976 end-page: 164 ident: CR16 article-title: Option pricing when underlying stock returns are discontinuous publication-title: Journal of Financial Econometrics doi: 10.1016/0304-405X(76)90023-4 – volume: 3 start-page: 227 year: 1999 end-page: 236 ident: CR17 article-title: Optional stopping for a diffusion with jumps publication-title: Finance and Stochastics doi: 10.1007/s007800050060 – volume: 1 start-page: 21 year: 1993 end-page: 31 ident: CR11 article-title: Efficient procedures for valuing European and American path-dependent options publication-title: Journal of Derivatives doi: 10.3905/jod.1993.407869 – volume: 330 start-page: 10 year: 2007 end-page: 23 ident: CR13 article-title: Convergence of the binomial tree method for Asian options in jump-diffusion models publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/j.jmaa.2006.07.042 – volume: 156 start-page: 23 year: 2003 end-page: 45 ident: CR21 article-title: Numerical Analysis on binomial tree methods for a jump-diffusion model publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(02)00903-2 – volume: 27 start-page: 1 year: 1992 end-page: 67 ident: CR8 article-title: User’s guide to viscosity solutions of second order partial differential equations publication-title: Bulletin of American Mathematical Society doi: 10.1090/S0273-0979-1992-00266-5 – volume: 16 start-page: 173 year: 1997 ident: 10.1016/j.jkss.2009.07.002_b6 article-title: Currency lookback options and observation frequency: A binomial approach publication-title: Journal of International Money and Finance doi: 10.1016/S0261-5606(96)00052-6 – volume: 16 start-page: 445 year: 2000 ident: 10.1016/j.jkss.2009.07.002_b9 article-title: A modified binomial tree method for currency lookback options publication-title: Acta Mathematica Sinica doi: 10.1007/s101140000068 – volume: 6 start-page: 17 year: 1996 ident: 10.1016/j.jkss.2009.07.002_b5 article-title: Pricing of American Path-dependent Contingent Claims publication-title: Mathematical Finance doi: 10.1111/j.1467-9965.1996.tb00111.x – volume: 1 start-page: 271 year: 1991 ident: 10.1016/j.jkss.2009.07.002_b4 article-title: Convergence of approximation schemes for fully nonlinear second order equations publication-title: Asymptotic Analysis doi: 10.3233/ASY-1991-4305 – volume: 330 start-page: 10 year: 2007 ident: 10.1016/j.jkss.2009.07.002_b13 article-title: Convergence of the binomial tree method for Asian options in jump-diffusion models publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/j.jmaa.2006.07.042 – volume: 35 start-page: 145 year: 1997 ident: 10.1016/j.jkss.2009.07.002_b19 article-title: Optimal stopping, free boundary and American option in a jump-diffusion model publication-title: Applied Mathematics and Optimization doi: 10.1007/s002459900042 – volume: 27 start-page: 1 year: 1992 ident: 10.1016/j.jkss.2009.07.002_b8 article-title: User’s guide to viscosity solutions of second order partial differential equations publication-title: Bulletin of American Mathematical Society doi: 10.1090/S0273-0979-1992-00266-5 – ident: 10.1016/j.jkss.2009.07.002_b18 – volume: 156 start-page: 23 year: 2003 ident: 10.1016/j.jkss.2009.07.002_b21 article-title: Numerical Analysis on binomial tree methods for a jump-diffusion model publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(02)00903-2 – volume: 48 start-page: 1086 year: 2002 ident: 10.1016/j.jkss.2009.07.002_b14 article-title: A jump diffusion model for option pricing publication-title: Management Science doi: 10.1287/mnsc.48.8.1086.166 – volume: 3 start-page: 227 year: 1999 ident: 10.1016/j.jkss.2009.07.002_b17 article-title: Optional stopping for a diffusion with jumps publication-title: Finance and Stochastics doi: 10.1007/s007800050060 – volume: 3 start-page: 145 year: 1976 ident: 10.1016/j.jkss.2009.07.002_b16 article-title: Option pricing when underlying stock returns are discontinuous publication-title: Journal of Financial Econometrics – volume: 48 start-page: 1833 year: 1993 ident: 10.1016/j.jkss.2009.07.002_b2 article-title: Jump diffusion option valuation in discrete time publication-title: Journal of Finance doi: 10.2307/2329069 – volume: 34 start-page: 1111 year: 1979 ident: 10.1016/j.jkss.2009.07.002_b10 article-title: Path dependent options: Buy at the Low, Sell at the High publication-title: Journal of Finance doi: 10.2307/2327238 – volume: 32 start-page: 612 year: 1994 ident: 10.1016/j.jkss.2009.07.002_b3 article-title: Optimal control of the L norm of a diffusion process publication-title: SIAM Journal on Control and Optimization doi: 10.1137/S0363012991223595 – volume: 42 start-page: 1899 year: 2005 ident: 10.1016/j.jkss.2009.07.002_b20 article-title: Convergence of the binomial tree method for American options in a jump-diffusion model publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/S0036142902409744 – volume: 7 start-page: 229 year: 1979 ident: 10.1016/j.jkss.2009.07.002_b7 article-title: Option pricing: A simplified approach publication-title: Journal of Financial Econometrics doi: 10.1016/0304-405X(79)90015-1 – volume: 50 start-page: 1178 year: 2004 ident: 10.1016/j.jkss.2009.07.002_b15 article-title: Option pricing under a double exponential jump diffusion model publication-title: Management Science doi: 10.1287/mnsc.1030.0163 – volume: 13 start-page: 293 year: 1996 ident: 10.1016/j.jkss.2009.07.002_b1 article-title: Viscosity solution of nonlinear integro-differential equations publication-title: Annales de l’Institut Henri Poincaré Analyse Non Linéaire doi: 10.1016/S0294-1449(16)30106-8 – volume: 42 start-page: 1094 year: 2004 ident: 10.1016/j.jkss.2009.07.002_b12 article-title: Convergence of binomial tree method for European/American path-dependent options publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/S0036142902414220 – volume: 1 start-page: 21 year: 1993 ident: 10.1016/j.jkss.2009.07.002_b11 article-title: Efficient procedures for valuing European and American path-dependent options publication-title: Journal of Derivatives doi: 10.3905/jod.1993.407869 |
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| Snippet | We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M.,... We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M.,... |
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| StartPage | 397 |
| SubjectTerms | Adjusted binomial tree method Applied Statistics Bayesian Inference Exponential jumps Lookback option Partial integro-differential equation Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Stochastic differential equation Viscosity solution 통계학 |
| Title | Analytical binomial lookback options with double-exponential jumps |
| URI | https://dx.doi.org/10.1016/j.jkss.2009.07.002 https://link.springer.com/article/10.1016/j.jkss.2009.07.002 https://www.kci.go.kr/kciportal/ci/sereArticleSearch/ciSereArtiView.kci?sereArticleSearchBean.artiId=ART001412691 |
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| ispartofPNX | Journal of the Korean Statistical Society, 2009, 38(4), , pp.397-404 |
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