Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options

Published Online:https://doi.org/10.1287/mnsc.1080.0953

References

  • Ahrens J. H., Dieter U. Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing (1974) 12:223–246CrossrefGoogle Scholar
  • Avramidis A. N., L'Ecuyer P. Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model. Management Sci. (2006) 52(12):1930–1944LinkGoogle 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) 319–326CrossrefGoogle Scholar
  • Barrera J., Huillet T., Paroissin C. Size-biased permutation of Dirichlet partitions and search-cost distribution. Probab. Engrg. Informational Sci. (2005) 19:83–97CrossrefGoogle Scholar
  • Best D. J. A note on gamma variate generators with shape parameter less than unity. Computing (1983) 30:185–188CrossrefGoogle Scholar
  • Boyle P., Broadie M., Glasserman P. Monte Carlo methods for security pricing. J. Econom. Dynam. Control (1997) 21(8–9):1276–1321CrossrefGoogle Scholar
  • Bratley P., Fox B. ALGORITHM 659: Implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Software (1988) 14(1):88–100CrossrefGoogle Scholar
  • Caflisch R. E., Morokoff W., Owen A. Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. J. Computational Finance (1997) 1(1):27–46CrossrefGoogle Scholar
  • Carr P., Géman H., Madan D., Yor M. The fine structure of asset returns: An empirical investigation. J. Bus. (2002) 75(2):305–332CrossrefGoogle Scholar
  • Chan T. Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Probab. (1999) 9:504–528CrossrefGoogle Scholar
  • Daal E., Madan D. An empirical examination of the Variance-Gamma Model for foreign currency options. J. Bus. (2005) 78(6):2121–2152CrossrefGoogle Scholar
  • Devroye L.Non-Uniform Random Variate Generation (1986) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Fiorani F. The Variance-Gamma process for option pricing. IV Workshop di Finanza Quantitativa (2003) (International Centre for Economic Research (ICER), Torina, Italy) . http://www.icer.it/workshop/Fiorani.pdfGoogle Scholar
  • Fiorani F., Luciano E. Credit risk in pure jump structural models. (2006) . Working Paper 6, International Center for Economic Research, Torino, ItalyGoogle Scholar
  • Fu M., Fu M. C., Jarrow R. A., Yen J. J., Elliott R. J. Variance-Gamma and Monte Carlo. Advances in Mathematical Finance (2007) (Birkhäuser)21–35CrossrefGoogle Scholar
  • Glasserman P.Monte Carlo Methods in Financial Engineering (2004) (Springer, New York) CrossrefGoogle Scholar
  • Glynn P. W., Whitt W. The asymptotic efficiency of simulation estimators. Oper. Res. (1992) 40(3):505–520LinkGoogle Scholar
  • Hammersley J. M., Handscomb D. C.Monte Carlo Methods (1964) (Methuen, London) CrossrefGoogle Scholar
  • Hirsa A., Madan D. B. Pricing American options under variance gamma. J. Computational Finance (2004) 7(2):63–80CrossrefGoogle Scholar
  • Hirth U. M. A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method. Bernoulli (1997) 3(2):225–232CrossrefGoogle Scholar
  • Hurd T. R. Credit risk modelling using time-changed Brownian motion. Further Developments in Quantitative Finance Workshop (2007) (International Centre for Mathematical Sciences (ICMS), Edinburgh, UK) . http://www.math.mcmaster.ca/tom/HurdTCBM.pdfGoogle Scholar
  • Joe S., Kuo F. Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Software (2003) 29(1):49–57CrossrefGoogle Scholar
  • Johnson N., Kotz S., Balakrishnan N.Discrete Multivariate Distributions (1997) (John Wiley & Sons, New York) Google Scholar
  • Kingman J. F. C. Random discrete distributions. J. Roy. Statist. Soc. B (1975) 37:1–22Google Scholar
  • Kingman J. F. C.Poisson Processes (1993) (Clarendon Press, Oxford) Google Scholar
  • Knuth D.The Art of Computer Programmming, Vol. 2: Seminumerical Algorithms (1997) 3rd ed.(Addison Wesley, Oxford, UK) Google Scholar
  • Kotz S., Balakrishnan N., Johnson N.Continuous Multivariate Distributions (2000) 2nd ed.(John Wiley & Sons, New York) CrossrefGoogle Scholar
  • L'Ecuyer P., Lemieux C., Dror M., L'Ecuyer P., Szidarovszki F. Recent advances in randomized Quasi-Monte Carlo methods. Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications (2002) (Kluwer Academic Publishers, Boston) 419–474CrossrefGoogle Scholar
  • L'Ecuyer P., Simard R. Inverting the symmetrical beta distribution. ACM Trans. Math. Software (2006) 32(4):509–520CrossrefGoogle Scholar
  • Madan D. B., Milne F. Option pricing with VG martingale components. Math. Finance (1991) 1:39–45CrossrefGoogle Scholar
  • Madan D. B., Seneta E. The variance gamma (VG) model for share market returns. J. Bus. (1990) 63:511–24CrossrefGoogle Scholar
  • Madan D. B., Carr P., Chang E. The variance gamma process and option pricing. Eur. Finance Rev. (1998) 2:79–105CrossrefGoogle Scholar
  • Marsaglia G., Tsang W. W. Some difficult-to-pass tests of randomness. J. Statist. Software (2002) 7(3):1–9CrossrefGoogle Scholar
  • Marsaglia G., Tsang W. W. The 64-bit universal RNG. Statist. Probab. Lett. (2004) 66(2):183–187CrossrefGoogle Scholar
  • Moskowitz B., Caflisch R. E. Smoothness and dimension reduction in quasi-Monte Carlo methods. J. Math. Comp. Model. (1996) 23:37–54CrossrefGoogle Scholar
  • Ökten G., Eastman W. Randomized quasi-Monte Carlo methods in pricing securities. J. Econom. Dynam. Control (2004) 28:2399–2426CrossrefGoogle 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):81–100CrossrefGoogle Scholar
  • Seneta E. Fitting the variance-gamma model to financial data. J. Appl. Probab. (2004) 41A:177–187CrossrefGoogle Scholar
  • Stein H., Hogan A., Carr P. Time for a change: The Variance-Gamma model and option pricing. (2007) . Working paper, Bloomberg Financial Markets, New York, http://ssrn.com/abstract=956625Google Scholar
  • Wilks S. S.Mathematical Statistics (1962) (Wiley, New York) Google Scholar
  • Yor M., Fu M. C., Jarrow R. A., Yen J. J., Elliott R. J. Some remarkable properties of gamma processes. Advances in Mathematical Finance (2007) (Birkhäuser, Boston) 37–47CrossrefGoogle Scholar
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