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Sensitivity analysis for averaged asset price dynamics with gamma processes

By Reiichiro Kawai and Atsushi Takeuchi


The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform parameter. Our framework covers not only the continuous Asian option, but also European, discrete Asian, average strike Asian, weighted average, spread options, and geometric average Asian options. Numerical results are provided to illustrate the effectiveness of our formulas in Monte Carlo simulations, relative to finite difference approximation

Topics: Asian options, Esscher transform, gamma process, Greeks, Lévy process, Malliavin calculus
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.spl.2009.09.010
OAI identifier:

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