Monte Carlo simulation is widely used to numerically solve stochastic differential equations. Although the method is flexible and easy to implement, it may be slow to converge. Moreover, an inaccurate solution will result when using large time steps. The Seven League scheme [1], a deep learning-based numerical method, has been proposed to address these issues. This paper generalizes the scheme regarding parallel computing, particularly on Graphics Processing Units (GPUs), improving the computational speed.
ESR3 Graziana Colonna
In this article we consider XVA pricing models for European options that incorporate three stochastic factors, namely, the price of the underlying asset and the intensities of default of the investor and the hedger, with the corresponding stochastic differential equations (SDEs) that govern their dynamics
Counterparty credit risk has been recently incorporated in the pricing of financial derivatives by adding different adjustments, the set of which is referred as XVA. In the case of European options to consider stochastic default intensities, instead of constant ones, a three factor model arises.