Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-01-26
Physics
Condensed Matter
Statistical Mechanics
28 pages, 4 figures
Scientific paper
In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pricing of path dependent European options can be often reduced to recursive (or nested) one-dimensional integral calculations, the above perturbative moment expansion (PME) leads very quickly to excellent numerical solutions. In this paper, we present the basic ideas of the method and the relative applications to a variety of contracts, mainly: asian, reverse cliquet and barrier options. A comparison with other numerical techniques is also presented.
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