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Numerical methods for Lévy processes


  • N. Hilber


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


No abstract is available for this item.

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  • N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
  • Handle: RePEc:spr:finsto:v:13:y:2009:i:4:p:471-500
    DOI: 10.1007/s00780-009-0100-5

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    7. 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.
    8. 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.
    9. repec:dau:papers:123456789/1380 is not listed on IDEAS
    10. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    11. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    12. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    13. 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, July.
    14. 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 637-654, May-June.
    15. Topper, Jürgen, 2001. "Worst Case Pricing of Rainbow Options," Hannover Economic Papers (HEP) dp-217, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    16. 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.
    17. Leobacher G., 2006. "Stratified sampling and quasi-Monte Carlo simulation of Lévy processes," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 231-238, October.
    18. 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.
    19. Pierre L’Ecuyer, 2009. "Quasi-Monte Carlo methods with applications in finance," Finance and Stochastics, Springer, vol. 13(3), pages 307-349, September.
    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. Simona Sanfelici, 2004. "Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 125-151, December.
    22. 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.
    23. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    24. Nan Chen & Paul Glasserman, 2007. "Additive and multiplicative duals for American option pricing," Finance and Stochastics, Springer, vol. 11(2), pages 153-179, April.
    25. Helyette Geman & C. Peter M. Dilip Y. Marc, 2007. "Self decomposability and option pricing," Post-Print halshs-00144193, HAL.
    26. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    27. 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.
    28. 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.
    29. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    30. 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.
    31. 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. Kathrin Glau, 2015. "Feynman-Kac formula for L\'evy processes with discontinuous killing rate," Papers 1502.07531,, revised Nov 2015.
    2. Amel Bentata & Rama Cont, 2015. "Forward equations for option prices in semimartingale models," Finance and Stochastics, Springer, vol. 19(3), pages 617-651, July.
    3. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
    4. Maximilian Ga{ss} & Kathrin Glau, 2016. "A Flexible Galerkin Scheme for Option Pricing in L\'evy Models," Papers 1603.08216,
    5. Yuji Hishida & Kenji Yasutomi, 2009. "Asymptotic behavior of prices of path dependent options," Papers 0911.5579,
    6. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901,, revised Oct 2016.
    7. Kathrin Glau, 2016. "A Feynman–Kac-type formula for Lévy processes with discontinuous killing rates," Finance and Stochastics, Springer, vol. 20(4), pages 1021-1059, October.
    8. Hepperger, Peter, 2012. "Hedging electricity swaptions using partial integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 600-622.
    9. repec:eee:spapps:v:127:y:2017:i:7:p:2208-2242 is not listed on IDEAS

    More about this item


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

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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