Effective Sub-Simulation-Free Upper Bounds for the Monte Carlo Pricing of Callable Derivatives and Various Improvements to Existing Methodologies

Abstract

We present a new non-nested approach to computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is is possible to early terminate paths once points of optimal exercise have been reached. A natural control variate for the multiplicative upper bound is introduced which renders it competitive to the additive one. In addition, a new bi-iterative family of upper bounds is introduced which take a stopping time, an upper bound, and a martingale as inputs.