Efficient Monte Carlo and Quasi–Monte Carlo Option Pricing Under the Variance Gamma Model

References

• Acworth P., Broadie M., Glasserman P., Hellekalek P., Niederreiter H. A comparison of some Monte Carlo and quasi-Monte Carlo techniques for option pricing. Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Number 127 in Lecture Notes in Statistics (1997) (Springer-Verlag, New York) 1–18Google Scholar
• Åkesson F., Lehoczy J. P. Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Sci. (2000) 46:1171–1187Link, Google Scholar
• Asmussen S. Stochastic simulation, with a view toward stochastic processes. (1999) . MaPhySto Lecture Notes 2, University of Aarhus, Aarhus, DenmarkGoogle Scholar
• Avramidis A. N., Ingalls R. G., Rossetti M. D., Smith J. S., Peters B. A. Efficient pricing of barrier options with the variance gamma model. Proc. 2004 Winter Simulation Conf. (2004) (IEEE Press, Piscataway, NJ) 1574–1578Crossref, Google Scholar
• Avramidis A. N., L’Ecuyer P., Tremblay P.-A. Efficient simulation of gamma and variance-gamma processes. Proc. 2003 Winter Simulation Conf. (2003) (IEEE Press, Piscataway, NJ) 319–326Crossref, Google Scholar
• Barndorff-Nielsen O. E. Processes of normal inverse Gaussian type. Finance Stochastics (1998) 2:41–68Crossref, Google Scholar
• Bertoin J.Lévy Processes (1998) (Cambridge University Press, Cambridge, UK) Google Scholar
• Blair J. M., Edwards C. A., Johnson J. H. Rational Chebyshev approximations for the inverse of the error function. Math. Comput. (1976) 30:827–830Crossref, Google Scholar
• Boyle P., Broadie M., Glasserman P. Monte Carlo methods for security pricing. J. Econom. Dynam. Control (1997) 21(8–9):1267–1321Crossref, Google Scholar
• Caflisch R. E., Moskowitz B., Niederreiter H., Shiue P. J.-S. Modified Monte Carlo methods using quasi-random sequences. Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Number 106 in Lecture Notes in Statistics (1995) (Springer-Verlag, New York) 1–16Crossref, Google Scholar
• Carr P., Madan D. Option valuation using the fast Fourier transform. J. Comput. Finance (1999) 2:61–73Crossref, Google Scholar
• Carr P., Geman H., Madan D., Yor M. The fine structure of asset returns: An empirical investigation. J. Bus. (2002) 75:305–332Crossref, Google Scholar
• Conte S. D., de Boor C.Elementary Numerical Analysis: An Algorithmic Approach (1972) 2nd ed.(McGraw-Hill, New York) Google Scholar
• Glasserman P.Monte Carlo Methods in Financial Engineering (2004) (Springer-Verlag, New York) Google Scholar
• Hirsa A., Madan D. B. Pricing American options under variance gamma. J. Comput. Finance (2004) 7(2):63–80Crossref, Google Scholar
• Hörmann W., Leydold J., Derflinger G.Automatic Nonuniform Random Variate Generation (2004) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Hull J.Options, Futures, and Other Derivative Securities (2000) 4th ed.(Prentice-Hall, Englewood-Cliff, NJ) Google Scholar
• Joyce D. C. Survey of extrapolation processes in numerical analysis. SIAM Rev. (1971) 13(4):435–490Crossref, Google Scholar
• Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, New York) Google Scholar
• L’Ecuyer P., Ingalls R. G., Rossetti M. D., Smith J. S., Peters B. A. Quasi-Monte Carlo methods in finance. Proc. 2004 Winter Simulation Conf. (2004a) (IEEE Press, Piscataway, NJ) 1645–1655Crossref, Google Scholar
• L’Ecuyer P. SSJ: A Java library for stochastic simulation. (2004b) . Software user’s guide, University of Montréal, Montréal, Canada, http://www.iro.umontreal.ca∼lecuyerGoogle Scholar
• L’Ecuyer P., Lemieux C., Dror M., L’Ecuyer P., Szidarovszky F. Recent advances in randomized quasi-Monte Carlo methods. Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications (2002) (Kluwer Academic Publishers, Boston, MA) 419–474Crossref, Google Scholar
• L’Ecuyer P., Simard R. Inverting the symmetrical beta distribution. ACM Trans. Math. Software (2004) . ForthcomingGoogle Scholar
• Madan D. B., Milne F. Option pricing with V.G. martingale components. Math. Finance (1991) 1:39–55Crossref, Google Scholar
• Madan D. B., Seneta E. The variance gamma (V.G.) model for share market returns. J. Bus. (1990) 63:511–524Crossref, Google Scholar
• Madan D. B., Carr P. P., Chang E. C. The variance gamma process and option pricing. Eur. Finance Rev. (1998) 2:79–105Crossref, Google Scholar
• Moshier S. L. Cephes math library. (2000) . Retrieved August 7, 2006, http://www.moshier.netGoogle Scholar
• Moskowitz B., Caflisch R. E. Smoothness and dimension reduction in quasi-Monte Carlo methods. J. Math. Comput. Model. (1996) 23:37–54Crossref, Google Scholar
• Owen A. B. Latin supercube sampling for very high-dimensional simulations. ACM Trans. Model. Comput. Simulation (1998) 8(1):71–102Crossref, Google Scholar
• Owen A. B. Variance with alternative scramblings of digital nets. ACM Trans. Model. Comput. Simulation (2003) 13(4):363–378Crossref, Google Scholar
• Panneton F. Construction d’ensembles de points basée sur des récurrences linéaires dans un corps fini de caractéristique 2 pour la simulation Monte Carlo et l’intégration quasi-Monte Carlo. (2004) . Unpublished doctoral thesis, Département d’informatique et de recherche opérationnelle, Université de Montréal, CanadaGoogle Scholar
• Ribeiro C., Webber N. Correcting for simulation bias in Monte Carlo methods to value exotic options in models driven by Lévy processes. (2003) . Working paper, Cass Business School, London, UKGoogle Scholar
• Ribeiro C., Webber N. Valuing path-dependent options in the variance-gamma model by Monte Carlo with a gamma bridge. J. Computational Finance (2004) 7(2):81–100Crossref, Google Scholar