The Least-Squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001) prices American options with a regression-based early-exercise strategy. This paper analyzes LSM estimator variance to identify two sources: sampling design and stopping time estimation. We examine the effect of...

We establish simple analytical and numerical methods for propagating stochastic price processes backwards in time, step by step, to the initial value while satisfying all cross-sectional and serial requirements. This proves useful in dealing with complex path-dependent options with American...

This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options...

Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least...

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...