Asia-Pacific Financial Markets

, Volume 13, Issue 4, pp 327–344 | Cite as

Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes

  • Jérémy Poirot
  • Peter TankovEmail author


Lévy processes are popular models for stock price behavior since they allow to take into account jump risk and reproduce the implied volatility smile. In this paper, we focus on the tempered stable (also known as CGMY) processes, which form a flexible 6-parameter family of Lévy processes with infinite jump intensity. It is shown that under an appropriate equivalent probability measure a tempered stable process becomes a stable process whose increments can be simulated exactly. This provides a fast Monte Carlo algorithm for computing the expectation of any functional of tempered stable process. We use our method to price European options and compare the results to a recent approximate simulation method for tempered stable process by Madan and Yor (CGMY and Meixner Subordinators are absolutely continuous with respect to one sided stable subordinators, 2005).


Monte Carlo Option pricing Lévy process Tempered stable process CGMY model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asmussen S., Rosiński J. (2001). Approximations of small jumps of Lévy processes with a view towards simulation. Journal of Applied. Probability 38, 482–493CrossRefGoogle Scholar
  2. Boyarchenko S., Levendorskiĭ S. (2002). Non-Gaussian Merton-Black-Scholes theory. River Edge, NJ, World ScientificGoogle Scholar
  3. Carr P., Geman H., Madan D., Yor M. (2002). The fine structure of asset returns: An empirical investigation. Journal of Business 75, 305–332CrossRefGoogle Scholar
  4. Carr P., Madan D. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance 2: 61–73Google Scholar
  5. Chambers J., Mallows C., Stuck B. (1976). A method of simulating stable random variables. Journal of American Statistical Assiciation 71, 340–344CrossRefGoogle Scholar
  6. Cont, R., Bouchaud, J.-P., & Potters, M. (1997). Scaling in financial data: Stable laws and beyond. In: B. Dubrulle, F. Graner, & D. Sornette (Eds.), Scale invariance and beyond. Berlin: Springer.Google Scholar
  7. Cont R., Tankov P. (2004). Financial modelling with jump processes. Boca Raton, FL, Chapman & Hall/CRC PressGoogle Scholar
  8. Cont R., Voltchkova E. (2005). A finite difference scheme for option pricing in jump-diffusion and exponential Lévy models. SIAM Journal on Numerical Analysis 43, 1596–1626CrossRefGoogle Scholar
  9. Gradshetyn I., Ryzhik I. (1995). Table of integrals, series and products. San Diego, DA, Academic PressGoogle Scholar
  10. Koponen I. (1995). Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process. Physical Review E 52: 1197–1199CrossRefGoogle Scholar
  11. Madan, D. B., & Yor, M. (2005). CGMY and Meixner subordinators are absolutely continuous with respect to one sided stable subordinators. Prépublication du Laboratoire de Probabilités et Modèles Aléatoires.Google Scholar
  12. Rosiński, J. (2001). Series representations of Lévy processes from the perspective of point processes. In: O. Barndorff-Nielsen, T. Mikosch, & S. Resnick (Eds.), Lévy processes—theory and applications. Boston: Birkhäuser.Google Scholar
  13. Rosiński, J. (2004). Tempering stable processes. Preprint (cf.∼rosinski/manuscripts.html).Google Scholar
  14. Sato K. (1999). Lévy processes and infinitely divisible distributions. Cambridge, UK, Cambridge University PressGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.INRIARocquencourtFrance
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris 7ParisFrance

Personalised recommendations