Commodity Option Pricing: A Practitioner's Guide

2 Commodity Mathematics and Products

In this chapter, we shall start with the convenient framework of one-factor models familiar to all students of mathematical finance. After revising the familiar Black–Scholes analysis for traded spot markets, I shall show how this can be extended to forwards and futures markets, such as are encountered in commodities, together with a discussion of some peculiarities of these markets. Having discussed such linear products, we can go on to options – which is what this book is about! So thereafter, I shall describe some of the typical products encountered in commodity options markets together with techniques for their valuation under these models, and the chapter will conclude with a discussion of the more advanced models which appear in the literature.

2.1 SPOT, FORWARDS AND FUTURES

One of the main aspects that differentiates many (but not all) commodities from other asset classes is the absence of a traded spot contract. Typically a spot transaction is for settlement a few good business days in the future (T+2 is customary in FX and, more relevantly, for precious and base metals; T+5 is usual in energy). Let us consider the metals. This means that if a spot trade is entered into on Monday 10 September 2012, then settlement will occur on Wednesday 12 September 2012. By settlement, we mean that the required cashflows and exchanges of commodities of value are scheduled to occur on that date. As the trade date advances forward in time, the spot ...