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Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options

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  • Jaehyuk Choi

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.

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  • Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:6:p:627-644
    DOI: 10.1002/fut.21909
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    Cited by:

    1. Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    2. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    3. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    4. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    5. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    6. Anatoliy A. Pogorui & Anatoliy Swishchuk & Ramón M. Rodríguez-Dagnino, 2022. "Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations," Mathematics, MDPI, vol. 10(13), pages 1-14, June.

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