Arbitrage-Free Valuation of Energy Derivatives

Kaushik Amin, Victor Ng and Craig Pirrong

The great expansion in the variety and the volume of trading in energy derivatives in recent years has created a need for new analytical tools to price energy-contingent claims. In this chapter, we review some of the relevant techniques available in the literature to value energy claims, and we develop an arbitrage-free framework to value energy derivatives.

In particular, we focus on models that take the current term structure of futures or forward prices as given, and then value options and other types of derivatives based on this term structure. The use of the entire term structure makes the models more general than the standard Black (1976) model that is often used to price commodity-contingent claims. Moreover, the simultaneous modelling of the evolution of the entire term structure unifies the pricing and risk management of a portfolio of energy derivative positions. This is of great practical importance to the market participants who trade these claims.

Since we are interested in valuing claims that are based on the entire term structure of futures prices, we first need to understand the relationship between futures contracts of different maturities. This will provide