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Computing exponential moments of the discrete maximum of a Lévy process and lookback options

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  • Liming Feng & Vadim Linetsky, 2009. "Computing exponential moments of the discrete maximum of a Lévy process and lookback options," Finance and Stochastics, Springer, vol. 13(4), pages 501-529, September.
    • Handle: RePEc:spr:finsto:v:13:y:2009:i:4:p:501-529
    DOI: 10.1007/s00780-009-0096-x
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.
    3. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    4. Vadim Linetsky, 2004. "Lookback options and diffusion hitting times: A spectral expansion approach," Finance and Stochastics, Springer, vol. 8(3), pages 373-398, August.
    5. Farid Aitsahlia & Tzeung Le Lai, 1998. "Random walk duality and the valuation of discrete lookback options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 227-240.
    6. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    7. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
    10. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, January.
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    Cited by:

    1. Cai, Ning & Li, Chenxu & Shi, Chao, 2021. "Pricing discretely monitored barrier options: When Malliavin calculus expansions meet Hilbert transforms," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    2. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2023. "Partial quanto lookback options," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    3. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    4. Yingda Song & Ning Cai & Steven Kou, 2018. "Computable Error Bounds of Laplace Inversion for Pricing Asian Options," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 634-645, January.
    5. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    6. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    7. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema," Papers 2211.07765, arXiv.org.
    8. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2019. "Hilbert transform, spectral filters and option pricing," Annals of Operations Research, Springer, vol. 282(1), pages 273-298, November.
    9. Pingping Zeng & Yue Kuen Kwok & Wendong Zheng, 2015. "Fast Hilbert Transform Algorithms For Pricing Discrete Timer Options Under Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-26, November.
    10. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
    11. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    12. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Jie Chen & Liaoyuan Fan & Lingfei Li & Gongqiu Zhang, 2022. "A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation," Review of Derivatives Research, Springer, vol. 25(2), pages 189-232, July.
    14. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    15. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    16. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    17. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient inverse $Z$-transform and pricing barrier and lookback options with discrete monitoring," Papers 2207.02858, arXiv.org, revised Jul 2022.
    18. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models," Papers 2312.03915, arXiv.org.
    19. Lingfei Li & Vadim Linetsky, 2012. "Time-Changed Ornstein-Uhlenbeck Processes And Their Applications In Commodity Derivative Models," Papers 1204.3679, arXiv.org.

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    More about this item

    Keywords

    Lévy processes; Discrete maximum; Exponential moments; Esscher transform; Discrete lookback options; Fourier transform; Hilbert transform; Sinc expansion; 60G70; 60J75; 65T99; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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