Pricing bounds for discrete arithmetic Asian options under Lévy models |
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Authors: | D Lemmens LZJ Liang A De Schepper |
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Institution: | a TQC, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen, Belgiumb Lyman Laboratory of Physics, Harvard University, Cambridge MA 02138, USAc Faculty of Applied Economics & StatUa Statistics Center, Universiteit Antwerpen, Prinsstraat 13, 2000 Antwerpen, Belgium |
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Abstract: | Analytical bounds for Asian options are almost exclusively available in the Black-Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds. |
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Keywords: | Asian options Analytical bounds Lé vy models |
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