The additive Bachelier model with an application to the oil option market in the Covid period

TL;DR

This paper introduces a simple, three-parameter additive Bachelier model that accurately captures the implied volatility surface of oil options during the volatile Covid period, ensuring no-arbitrage and enabling efficient pricing.

Contribution

The paper presents a novel additive Bachelier model with closed-form solutions, ensuring no-arbitrage and capturing key features of the oil option market during Covid-19.

Findings

Model accurately fits the volatility surface during Covid-19

Ensures no-arbitrage condition in volatile markets

Enables efficient pricing of exotic options

Abstract

In April 2020, the Chicago Mercantile Exchange temporarily switched the pricing formula for West Texas Intermediate oil market options from the Black model to the Bachelier model. In this context, we introduce an additive Bachelier model that provides a simple closed-form solution and a good description of the implied volatility surface. This new additive model exhibits several notable mathematical and financial properties. It ensures the no-arbitrage condition, a critical requirement in highly volatile markets, while also enabling a parsimonious synthesis of the volatility surface. The model features only three parameters, each with a clear financial interpretation: the volatility term structure, the vol-of-vol, and a parameter for modelling skew. Model calibration can follow a cascade procedure: first, it accurately replicates the term structures of forwards and At-The-Money volatilities observed in the market; second, it fits the smile of the volatility surface. The proposed model also supports efficient pricing of path-dependent exotic options via Monte Carlo simulation, using a straightforward and computationally efficient approach. Overall, this model provides a robust and parsimonious description of the oil option market during the exceptionally volatile first period of the Covid-19 pandemic.