Likelihood ratio gradient estimation for Meixner distribution and Lévy processes
We address the problem of gradient estimation with respect to four characterizing parameters of the Meixner distribution and Lévy process. With the help of the explicit marginal probability density function, the likelihood ratio method is directly applicable, while unbiased estimators may contain infinite random series in their score function. We quantify the estimator bias arising when the infinite series is truncated to finite term. We further propose a substantially simple exact simulation method for the Meixner distribution, based on acceptance-rejection sampling and the Esscher density transform. Numerical results are presented in the context of financial Greeks to illustrate the effectiveness of our formulas along with bias estimates. Copyright Springer-Verlag 2012
Volume (Year): 27 (2012)
Issue (Month): 4 (December)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/statistics/journal/180/PS2|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, 05.
- Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:27:y:2012:i:4:p:739-755. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.