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COMPARISON OF NUMERICAL METHODS FOR OPTION PRICING UNDER THE CGMY MODEL

  • Lee, Ahram (Department of Mathematics Chungnam National University) ;
  • Lee, Younhee (Department of Mathematics Chungnam National University)
  • Received : 2016.06.28
  • Accepted : 2016.07.29
  • Published : 2016.08.15

Abstract

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

Keywords

References

  1. F. Black and M. S. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), 637-654. https://doi.org/10.1086/260062
  2. P. Carr, H. Geman, D. B. Madan, and M. Yor, The fine structure of asset returns: An empirical investigation, J. Bus. 75 (2002), 305-332. https://doi.org/10.1086/338705
  3. P. Carr and D. B. Madan, Option valuation using the fast Fourier transform, J. Comput. Financ. 2 (1999), 61-73. https://doi.org/10.21314/JCF.1999.043
  4. R. Cont and E. Voltchkova, A finite difference scheme for option pricing in jump diffusion and exponential Levy models, SIAM J. Numer. Anal. 43 (2005), 1596-1626. https://doi.org/10.1137/S0036142903436186
  5. J. Lee and Y. Lee, Tridiagonal implicit method to evaluate European and American options under infinite activity Levy models, J. Comput. Appl. Math. 237 (2013), 234-243. https://doi.org/10.1016/j.cam.2012.07.028
  6. S. Salmi and J. Toivanen, IMEX schemes for pricing options under jump-diffusion models, Appl. Numer. Math. 84 (2014), 33-45. https://doi.org/10.1016/j.apnum.2014.05.007
  7. I. R. Wang, J. W. L. Wan, and P. A. Forsyth, Robust numerical valuation of European and American options under the CGMY process, J. Comput. Financ. 10 (2007), 31-69. https://doi.org/10.21314/JCF.2007.169