A Two Factor Forward Curve Model with Stochastic Volatility for Commodity Prices

TL;DR

This paper introduces a forward curve model for commodity prices incorporating mean reversion, decorrelation, and stochastic volatility, with efficient numerical and Monte Carlo pricing methods for derivatives.

Contribution

It presents a novel two-factor forward curve model with stochastic volatility, capturing key market features and providing efficient pricing algorithms for complex derivatives.

Findings

Model captures mean reversion and Samuelson effect

Efficient numerical scheme for vanilla and early-exercise options

Monte Carlo pricing with drift approximation for complex derivatives

Abstract

We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of forward prices - rather than a "spot model" that models the evolution of the spot commodity price. Two Brownian motions drive moves across the forward curve, with a third Heston-like stochastic volatility process scaling instantaneous volatilities of all forward prices. In addition to an efficient numerical scheme for calculating European vanilla and early-exercise option prices, we describe an algorithm for Monte Carlo-based pricing of more generic derivative payoffs which involves an efficient approximation for the risk neutral drift that avoids having to simulate drifts for every forward settlement date required for pricing.