The 2015 AMMCS-CAIMS Congress
Interdisciplinary AMMCS Conference Series
Waterloo, Ontario, Canada | June 7-12, 2015AMMCS-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.