Approximations for Asian options in local volatility models |
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| Authors: | Paolo Foschi Stefano Pagliarani Andrea Pascucci |
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| Affiliation: | 1. Dipartimento di Scienze Statistiche “Paolo Fortunati”, Università di Bologna, Via Belle Arti 41, 40126 Bologna, Italy;2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy;3. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy |
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| Abstract: | We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat kernel expansion method in the framework of hypoelliptic, not uniformly parabolic, partial differential equations. |
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| Keywords: | Option pricing Analytical approximation Asian option Local volatility Hypoelliptic equation |
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