Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지
DOI QR코드

DOI QR Code

Simulation of the Shifted Poisson Distribution with an Application to the CEV Model

  • Kang, Chulmin (Center for Applications of Mathematical Principles, National Institute for Mathematical Sciences)
  • Received : 2014.04.30
  • Accepted : 2014.05.22
  • Published : 2014.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper introduces three different simulation algorithms of the shifted Poisson distribution. The first algorithm is the inverse transform method, the second is the rejection sampling, and the third is gamma-Poisson hierarchy sampling. Three algorithms have different regions of parameters at which they are efficient. We numerically compare those algorithms with different sets of parameters. As an application, we give a simulation method of the constant elasticity of variance model.

Keywords

References

  1. Abramowitz, M. and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, U.S. Government Printing Office, Washington, D.C., 1964.
  2. Cox, J. C. and S. A. Ross, "The valuation of options for alternative stochastic processes," Journal of Financial Economics 3, 1/2 (1976), 145-166. https://doi.org/10.1016/0304-405X(76)90023-4
  3. Delbaen, F. and H. Shirakawa, "A note on option pricing for the constant elasticity of variance model," Asia-Pacific Financial Markets 9, 2 (2002), 85-99. https://doi.org/10.1023/A:1022269617674
  4. Devroye, L., Non-uniform random variate generation, Springer-Verlag, New York, 1986.
  5. Fishman, G. S., Monte Carlo: concepts, algorithms, and applications, Springer Series on Operations Research, Springer-Verlag, New York, 1996.
  6. Going-Jaeschke, A. and M. Yor, "A survey and some generalizations of bessel processes," Bernoulli 9, 2 (2003), 313-349. https://doi.org/10.3150/bj/1068128980
  7. Lindsay, A. and D. Brecher, "Simulation of the CEV process and the local martingale property," Mathematics and Computers in Simulation 82, 5 (2012), 868-878. https://doi.org/10.1016/j.matcom.2011.12.006
  8. Makarov, R. and D. Glew, "Exact simulation of bessel diffusions," Monte Carlo Methods and Applications 16, 3/4 (2010), 283-306.
  9. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the art of scientific computing, 3rd edition, Cambridge University Press, Cambridge, 2007.