Pricing exotic options in a path integral approach |
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Authors: | G. Bormetti N. Moreni O. Nicrosini |
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Affiliation: | 1. Dipartimento di Fisica Nucleare e Teorica , Università di Pavia , Via A. Bassi 6, Pavia, 27100, Italy;2. Istituto Nazionale di Fisica Nucleare , Sezione di Pavia, Via A. Bassi 6, Pavia, 27100, Italy;3. CERMICS - ENPC , 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455, Marne la Vallée, Cedex 2, France |
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Abstract: | In the framework of the Black–Scholes–Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path-dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances. |
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Keywords: | Doubly stochastic binomial point process Relative volume Cox process Initial enlargement of filtration NYSE, New York Stock Exchange VWAP |
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