A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is...

Robust pricing of european options with wavelets and the characteristic function

We present a novel method for pricing European options based on the wavelet approximation method and the characteristic function. We focus on the discounted expected payoff pricing formula and compute it by means of wavelets. We approximate the density function associated to the underlying asset price process by a finite combination of jth order...

Option pricing with perturbation methods

This thesis discusses the use of perturbation theory in the context of financial mathematics, in particular on the use of matched asymptotic expansions in option pricing. Our methods are applied to the ordinary Black-Scholes model for illustration. In this simple example of the Black-Scholes model an exact solution is available, so it is in fact...