Sum of All Black-Scholes-Merton Models: An Efficient Pricing Method for Spread, Basket, and Asian Options
Journal of Futures Markets, 38(6):627-644, 2018
25 Pages Posted: 8 Feb 2017 Last revised: 2 Jun 2018
Date Written: February 7, 2017
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi-asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.
Keywords: Multi-Asset Black-Scholes-Merton, Spread Option, Basket Option, Asian Option, Curse of Dimensionality
JEL Classification: C52, C62, G13
Suggested Citation: Suggested Citation