Practical Option Valuations of Futures Contracts with Negative Underlying Prices

TL;DR

This paper introduces two alternative models, Ornstein-Uhlenbeck and continuous-time GARCH, for valuing European options on futures with potentially negative or mean-reverting underlying prices, addressing limitations of the Black 76 model.

Contribution

It proposes novel valuation models suitable for negative or mean-reverting underlying prices, expanding beyond traditional Black 76 assumptions.

Findings

OU and GARCH models provide more accurate valuations for negative underlying prices.

Comparison shows differences between new models and Black 76 in various market scenarios.

New models better capture mean reversion in underlying prices.

Abstract

Here we propose two alternatives to Black 76 to value European option future contracts in which the underlying market prices can be negative or mean reverting. The two proposed models are Ornstein-Uhlenbeck (OU) and continuous time GARCH (generalized autoregressive conditionally heteroscedastic). We then analyse the values and compare them with Black 76, the most commonly used model, when the underlying market prices are positive