In this overview chapter, we will discuss the use of exponentially converging option pricing techniques for option valuation. We will focus on the pricing of European options, and they are the basic instruments within a calibration procedure when fitting the parameters in asset dynamics. The numerical solution is governed by the solution of the discounted expectation of the pay-off function. For the computation of the expectation, we require knowledge about the corresponding probability density function, which is typically not available for relevant stochastic asset price processes. Many publications regarding highly efficient pricing of these contracts are available, where computation often takes place in the Fourier space. Methods based on quadrature and the Fast Fourier Transform (FFT) [1-3] and methods based on Fourier cosine expansions [4,5] have therefore been developed because for relevant log-asset price processes, the characteristic function appears to be available. The characteristic function is defined as the Fourier transform of the density function. Here, we wish to extend the overview by discussing the recently presented highly promising class of wavelet option pricing techniques, based on either B-splines or Shannon wavelets.

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Editor M.A.H. Dempster , J. Kanniainen (Juho) , J. Keane (John) , E. Vynckier (Erik)
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Maree, S.C, Ortiz Gracia, L, & Oosterlee, C.W. (2018). Fourier and wavelet option pricing methods. In M.A.H Dempster, J Kanniainen, J Keane, & E Vynckier (Eds.), High-Performance Computing in Finance: Problems, Methods, and Solutions (pp. 249–272). doi:10.1201/9781315372006