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

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University - HSBC School of Business

Date Written: February 7, 2017

Abstract

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

Choi, Jaehyuk, Sum of All Black-Scholes-Merton Models: An Efficient Pricing Method for Spread, Basket, and Asian Options (February 7, 2017). Journal of Futures Markets, 38(6):627-644, 2018, Available at SSRN: https://ssrn.com/abstract=2913048 or http://dx.doi.org/10.2139/ssrn.2913048

Jaehyuk Choi (Contact Author)

Peking University - HSBC School of Business ( email )

University Town
Shenzhen, Guangdong 518055
China

HOME PAGE: http://www.jaehyukchoi.net/phbs_en

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