Gradient Estimation and Mountain Range Options

Abstract

This application of gradient estimation drawn from financial engineering and ex- plores several exotic derivatives that are collectively known Mountain Range options, employing Monte Carlo simulation to price these options and developing gradient es- timates to study the sensitivities to underlying parameters, known as “the Greeks”. We find that IPA and LR/SF methods are efficient methods of gradient estimation for Mountain Range products at a considerably reduced computation cost compared with the commonly used finite difference methods.

Keywords: Monte Carlo Simulation,Option Pricing, Gradient Estimation, Mountain Range Options

JEL Classification: G12, C63