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Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach

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  • Liming Feng
  • Vadim Linetsky

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  • Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384.
  • Handle: RePEc:bla:mathfi:v:18:y:2008:i:3:p:337-384
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    4. 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.
    5. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    8. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    9. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, March.
    10. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    11. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    12. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    13. Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, vol. 49(8), pages 1071-1088, August.
    14. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    15. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
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    Cited by:

    1. repec:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500339 is not listed on IDEAS
    2. 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.
    3. repec:kap:revdev:v:20:y:2017:i:3:d:10.1007_s11147-017-9130-x is not listed on IDEAS
    4. Keegan Mendonca & Vasileios E. Kontosakos & Athanasios A. Pantelous & Konstantin M. Zuev, 2018. "Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation," Papers 1803.03364, arXiv.org, revised Mar 2018.
    5. Fuh, Cheng-Der & Luo, Sheng-Feng & Yen, Ju-Fang, 2013. "Pricing discrete path-dependent options under a double exponential jump–diffusion model," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2702-2713.
    6. Takayuki Sakuma & Yuji Yamada, 2014. "Application of Homotopy Analysis Method to Option Pricing Under Lévy Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(1), pages 1-14, March.
    7. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    8. 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.
    9. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    10. Julien Hok & Tat Lung Chan, 2016. "Option pricing with Legendre polynomials," Papers 1610.03086, arXiv.org, revised Mar 2017.
    11. Alev{s} v{C}ern'y, 2016. "Discrete-Time Quadratic Hedging of Barrier Options in Exponential L\'{e}vy Model," Papers 1603.03747, arXiv.org.
    12. 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.
    13. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," LSE Research Online Documents on Economics 67564, London School of Economics and Political Science, LSE Library.
    14. Gzyl, H. & Milev, M. & Tagliani, A., 2017. "Discontinuous payoff option pricing by Mellin transform: A probabilistic approach," Finance Research Letters, Elsevier, vol. 20(C), pages 281-288.
    15. repec:eee:ejores:v:262:y:2017:i:1:p:381-400 is not listed on IDEAS
    16. Lingfei Li & Vadim Linetsky, 2012. "Time-Changed Ornstein-Uhlenbeck Processes And Their Applications In Commodity Derivative Models," Papers 1204.3679, arXiv.org.
    17. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2017. "Fluctuation identities with continuous monitoring and their application to price barrier options," Papers 1712.00077, arXiv.org.
    18. Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.
    19. 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.

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