The 2015 AMMCS-CAIMS Congress
Interdisciplinary AMMCS Conference SeriesWaterloo, Ontario, Canada | June 7-12, 2015
AMMCS-CAIMS 2015 Plenary Talk
On Fourier cosine expansions and wavelets for derivative pricing and risk management in computational finance
Kees Oosterlee (Delft University of Technology and CWI)
In this talk, we discuss applications of Fourier cosine expansions and wavelets in computational finance. Next to the accurate and efficient valuation of various financial options, we recently generalized the methods towards risk management and the numerical solution of backward stochastic differential equations (BSDEs). Typically Fourier techniques in finance rely on the availability of the asset dynamics' characteristic function (ie. the Fourier transform of the asset's density function). We will discuss a numerical Fourier method for which the characteristic function need not be available. The resulting methods can then also be employed for problems with varying coefficients (local volatility, stochastic local volatility) models), such as for the Stochastic Alpha Beta Rho (SABR) method.
Prof. Kees Oosterlee (http://www.cwi.nl/people/2098, http://ta.twi.tudelft.nl/mf/users/oosterle/) works in numerical analysis and scientific computing at the CWI, center for mathematics and computer science, in Amsterdam, the Netherlands, as well as in the Delft University of Technology. His field of expertise is Computational Finance, working at the interface of numerical and financial mathematics. In Oosterlee’s group the COS method, pricing financial derivatives efficiently with Fourier cosine expansions, has been developed, which is in use at financial institutions world-wide. Prof. Oosterlee is the Editor-in-Chief of the Journal of Computational Finance. He has organized several international workshops and conferences, and taught Summer Schools abroad (in Spain, Japan, South Africa) on Computational Finance. His 90 journal publications range from multigrid solution methods for fluid flow problems to Monte Carlo methods in finance.