Analysis of Fourier transform valuation formulas and applications

Details Analysis of Fourier transform valuation formulas and applications Analysis of Fourier transform valuation formulas and applications

2008-09-19

arxiv.org/abs/0809.3405v4

Applied Mathematical Finance 2010, Vol. 17, No. 3, 211-240

Economy

Quantitative Finance

Pricing of Securities

26 pages, 3 figures, to appear in Appl. Math. Finance

Scientific paper

10.1080/13504860903326669

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.

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