We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based...

In this paper, we will present a multiple time-step Monte Carlo simulation technique for pricing options under the (Stochastic Alpha Beta Rho (SABR)) model. The proposed method is an extension of the one time-step Monte Carlo method that we proposed in an accompanying paper, for pricing European...

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the integrated variance (conditional on the SABR volatility process), using Fourier techniques and a copula. Resulting is a...

In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by...