Geometrical Approximation and Perturbative methods for PDEs in Finance

The book investigates the benefits of Spectral Methods, which are found to be an appealing numerical technique when the solution in closed form doesn't exist, but unfortunately it cannot be used in every case. A remarkable case in which it is possible to use the Spectral Methods is for pricing the Double Barrier Options as we have seen in Chapter 3. The main achievement of this work is the introduction of two methods, that we have called Geometrical Approximation and Perturbative Method respectively, by which is possible to evaluate the fair option prices in the Heston and SABR market model. Both proposed methods can be generalised to other market models and for pricing other derivatives contracts, although, in order to show the above methodologies, we have chosen to pricing Options of only two kinds: Vanilla Options and knock-out Barrier Options.

Expert of Stochastic Calculus and PDEs, currently external Professor of International Finance at Pisa University. Assignement teaching of Quantitative Finance and Stochastic Processes at Scuola Superiore Sant’Anna in Pisa. Advisor on HFT for italian Public Lawer. Advisor for Scientifica Hiring.