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Numerical methods for Lévy processes

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  • N. Hilber

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  • N. Reich
  • C. Schwab
  • C. Winter
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    Abstract

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    File URL: http://hdl.handle.net/10.1007/s00780-009-0100-5
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 13 (2009)
    Issue (Month): 4 (September)
    Pages: 471-500

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    Handle: RePEc:spr:finsto:v:13:y:2009:i:4:p:471-500

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    Related research

    Keywords: Multidimensional Lévy processes; Numerical methods; Asset pricing; 60J75; 65N06; 65N30; C63;

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    References

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    1. Elisa Luciano & Wim Schoutens, 2005. "A Multivariate Jump-Driven Financial Asset Model," ICER Working Papers - Applied Mathematics Series 6-2005, ICER - International Centre for Economic Research.
    2. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75.
    3. Pierre L’Ecuyer, 2009. "Quasi-Monte Carlo methods with applications in finance," Finance and Stochastics, Springer, vol. 13(3), pages 307-349, September.
    4. Yor, Marc & Madan, Dilip B. & Carr, Peter & Geman, Hélyette, 2007. "Self-decomposability and option pricing," Economics Papers from University Paris Dauphine 123456789/1380, Paris Dauphine University.
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Mulinacci, Sabrina, 1996. "An approximation of American option prices in a jump-diffusion model," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 1-17, March.
    7. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    8. Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 311-349, February.
    9. Kaushik Amin & Ajay Khanna, 1994. "Convergence Of American Option Values From Discrete- To Continuous-Time Financial Models," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 289-304.
    10. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    11. Claudia Ribeiro & Nick Webber, 2006. "Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 333-352.
    12. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
    13. Nan Chen & Paul Glasserman, 2007. "Additive and multiplicative duals for American option pricing," Finance and Stochastics, Springer, vol. 11(2), pages 153-179, April.
    14. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, 07.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    16. Stephen Figlewski & Bin Gao, 1998. "The Adaptive Mesh Model: A New Approach to Efficient Option Pricing," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-032, New York University, Leonard N. Stern School of Business-.
    17. Nina Boyarchenko & Sergei Levendorskiǐ, 2007. "On Errors And Bias Of Fourier Transform Methods In Quadratic Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 273-306.
    18. Simona Sanfelici, 2004. "Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff," Decisions in Economics and Finance, Springer, vol. 27(2), pages 125-151, December.
    19. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    20. Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
    21. Topper, Jürgen, 2001. "Worst Case Pricing of Rainbow Options," Hannover Economic Papers (HEP) dp-217, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    22. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    23. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.
    24. Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 131-152.
    25. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    26. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    27. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December.
    28. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
    29. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:
    1. Yuji Hishida & Kenji Yasutomi, 2009. "Asymptotic behavior of prices of path dependent options," Papers 0911.5579, arXiv.org.
    2. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Society for Computational Economics, vol. 40(1), pages 63-104, June.
    3. Hepperger, Peter, 2012. "Hedging electricity swaptions using partial integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 600-622.

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