Pricing Discretely Monitored Asian Options under Lévy Processes
نویسندگان
چکیده
We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using di¤erent parametric Lévy processes. We also discuss model-risk issues. JEL Classi cation: G13, C63 Keywords: Asian options, discrete monitoring, quadrature, Lévy processes, stable processes, model risk. This paper was reviewed and accepted while Prof. Giorgio Szego was the Managing Editor of The Journal of Banking and Finance and by the past Editorial Board. Corresponding Author: Gianluca Fusai, Dipartimento SEMEQ, Università degli Studi del Piemonte Orientale, Via Perrone 18, 28100 Novara, Italia; e-mail: [email protected], phone number: +39 0321 375312. Gianluca Fusai aknowledges the grant n. 2006132713 by the Italian Ministery of Scienti c Research.
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