Title: Efficient option pricing using the Fast Fourier transforms
Speaker: Yue Kuen KWOK, Department of Mathematics, Hong Kong University of Science and Technology
Time: 2:20pm, Sep 15 (Tue), 2009
Place: Room 110, CSIE building

Abstract:

The Fourier transform approach is an important tool in options pricing, and together with the Fast Fourier transform (FFT) algorithms, real time options pricing can be delivered. The underlying asset price processes can allow for more general realistic structure of asset returns, say, excess kurtosis and stochastic volatility. It is known that once the characteristic function of the risk neutral density is known analytically, the analytic expression for the Fourier transform of the option value can be derived. By treating option price analogous to a probability density function, option prices across the whole spectrum of strikes can be obtained via fast Fourier transform. Fourier transform is an effective tool to compute convolution products. We show how this property of the Fourier transform of a convolution product can be used to value various types of option pricing models. In particular, we show how one can price Bermudan style options under Levy processes using FFT techniques in an efficient manner by reformulating the risk neutral valuation formulation as a convolution. By extending the finite state Markov chain approach in option pricing, we illustrate an innovative FFT-based network tree approach for option pricing under Levy process. Similar to the forward shooting grid technique in the usual lattice tree algorithms, the approach can be adapted to valuation of options with exotic path dependence. Limitations of the FFT techniques are also addressed, like the difficulties in dealing with time dependent parameter functions and barrier type models. Sampling errors and truncation errors in numerical implementation of FFT are discussed. Some strategic issues in error bound minimization are also considered.


(This is a joint work with Kwai Sun LEUNG and Hoi Ying WONG, Chinese University of Hong Kong.)