Commodity volatility modelling and option pricing with a potential function approach

Abstract

We consider a novel approach to modelling of commodity prices and apply it to commodity option pricing and volatility estimation. This approach is particularly suited for prices with multiple attraction regions, such as crude oil and other energy and agricultural commodities. The price is modelled as a diffusion process governed by a potential function with minima at the attraction points. When applied to crude oil prices, the method captures characteristic behaviour of the prices remarkably well. Pricing of European options on spot and futures commodity contracts is developed within the potential model, and compared to the Black–Scholes framework. The approach provides a new way of estimating the volatility, which is particularly useful when option prices (and hence implied volatilities) are not readily available; this is often the case for commodity markets. European options on physical commodities and commodity futures are priced using the volatility forecasts obtained from the model. The performance of the model is evaluated on the basis of the hedging costs of an option. For options on crude oil, the method outperforms – in terms of hedging costs—the Black–Scholes approach with historical volatility.

Keywords:

• commodity prices
• multiple attraction regions
• potential function
• volatility esimation
• option pricing
• hedging costs