A Black-Scholes user's guide to the Bachelier model

TL;DR

This paper reviews the Bachelier model's application in commodity options, especially during COVID-19, and connects it with the Black-Scholes model through a unified framework for better risk management and pricing.

Contribution

It provides a comprehensive review of Bachelier's model, its practical applications, and introduces a unified displaced Black-Scholes model encompassing both models.

Findings

Bachelier model effectively handles negative prices.

Unified model spectrum aids in model selection.

Practical insights for volatility and barrier options pricing.

Abstract

To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges temporarily switched the option model from Black--Scholes to Bachelier in 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical results on volatility conversion, risk management, stochastic volatility, and barrier options pricing to facilitate the model transition. In particular, using the displaced Black-Scholes model as a model family with the Black-Scholes and Bachelier models as special cases, we not only connect the two models but also present a continuous spectrum of model choices.