The stochastic collocation Monte Carlo sampler: Highly efficient sampling from ‘expensive’ distributions

In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a...

A novel Monte Carlo approach to hybrid local volatility models

We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007,...

Arbitrage-free approaches for pricing interest rate derivatives under the SABR model

This thesis is about pricing swaptions under the SABR model or a variant thereof. In the interest market a stochastic local volatility is often used by practitioners to describe the volatility curve in the strike dimension of swaptions. It is a fast approach to inter- and extrapolate market quotes. It is however well-known that this approach is...