Commodity Option Pricing
eBook - ePub

Commodity Option Pricing

A Practitioner's Guide

Iain J. Clark

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eBook - ePub

Commodity Option Pricing

A Practitioner's Guide

Iain J. Clark

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About This Book

Commodity Option Pricing: A Practitioner's Guide covers commodity option pricing for quantitative analysts, traders or structurers in banks, hedge funds and commodity trading companies.

Based on the author's industry experience with commodity derivatives, this book provides a thorough and mathematical introduction to the various market conventions and models used in commodity option pricing. It introduces the various derivative products typically traded for commodities and describes how these models can be calibrated and used for pricing and risk management. This book has been developed with input from traders and features examples using real-world data, together with relevant up-to-date academic research.

This book includes practical descriptions of market conventions and quote codes used in commodity markets alongside typical products seen in broker quotes and used in calibration. Also discussed are commodity models and their mathematical derivation and volatility surface modelling for traded commodity derivatives. Gold, silver and other precious metals are addressed, including gold forward and gold lease rates, as well as copper, aluminium and other base metals, crude oil and natural gas, refined energy and electricity. There are also sections on the products encountered in commodities such as crack spread and spark spread options and alternative commodities such as carbon emissions, weather derivatives, bandwidth and telecommunications trading, plastics and freight.

Commodity Option Pricing is ideal for anyone working in commodities or aiming to make the transition into the area, as well as academics needing to familiarize themselves with the industry conventions of the commodity markets.

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At the time of the writing of this book, and since about the turn of the century, commodities have experienced a continued surge in both price (as shown in Figure 1.1) and interest in a world of increasingly scarce resources and rapid population growth together with demand growth in the rapidly industrialising emerging markets. This book is a practical quantitative analyst’s guide to how to get professionally involved in the world of commodities.
Figure 1.1 Price history of TR/J CRB Commodity Index (1994–2012, log-scale).
While the book is focused primarily on the market in commodity derivatives and the quantitative analysts (quants) who work in these markets, much commodity trading occurs through the vehicle of futures trading on organised exchanges, so I envisage this work will be of use to the traders, quant developers, structurers and finance professionals who work alongside the quants. Though this is first and foremost a practitioners’ book, I have attempted to put the material into context with regard to the literature in the area, which I believe will be of tangible benefit to academics and students of financial mathematics from all areas, who are interested in learning more about the fascinating world of commodities.
Although this is a technical book, I have attempted to make it as accessible as possible on several levels. One barrier to making the transition into commodities is the necessary, and unavoidable, jargon, which I have tried to cut through for the benefit of the reader (see the Glossary at the end of the book, for example). This I hope should set the avid reader on course to apply the theory from his or her studies to build the models and systems required to add real value to a commodities desk. Content has been developed using real-world data throughout and has been written in conjunction with both industry professionals and university lecturers in commodities.
Once again, the preferred mathematical background for the derivatives elements of this book is a familiarity with option pricing at the level of Hull (2011) and, ideally, Baxter and Rennie (1996). There is necessarily some overlap with my previous FX book (Clark, 2011) but this book is a standalone work and introduces the various commodity markets and develops the option pricing toolkit for commodity derivatives in a self-contained manner. This book is not purely mathematical, however; it is important to have some familiarity with the physical aspect of the various commodities also, in order to develop intuition and to have credibility when talking with traders (or in interviews). I have therefore attempted to relate the technical machinery back to the practical aspects throughout.
Producers, intermediaries and consumers are all exposed to risk. Additionally, some investors have been increasingly attracted towards speculative investment in some commodities due to the benefits of diversification and perceived underperformance in other asset classes. Finally, the durable physical aspect of some commodities (especially the metals and energy) may appeal to those who have lost money on purely financial investments during the collapse of the dot com equity bubble and the subprime financial crisis thereafter.
As well as trading the physical commodity itself, it is commonplace to trade financial contracts linked to commodities. Simple examples are futures contracts on oil and the base metals; more complicated are option contracts which provide the owner with the right but not the obligation to take profits on price moves in a particular direction. Commodity derivatives also allow participants in the financial markets to spread their risk exposure over the course of a calendar period, and to “lock-in” profits on a spread between the price of a refined product and an unrefined product.
This book shows how these derivatives are priced in the industry context. It is a practitioner’s guide which introduces commodity options, describing the features of the various commodity markets and what industry professionals need to know when developing option pricing analytics for trading desks and risk departments. What sort of products might one encounter? What typical price quotes might one obtain and have to calibrate a model to? What makes oil options different from precious metal or base metal options, for example.
These questions, and more, are the concern of this book.


The oldest financial markets are the commodity markets. By a commodity, we mean an undifferentiated physical item that satisfies an economic want or need. The oldest commodity markets are therefore the agricultural and metal markets – wheat, gold, etc. Energy (fossil fuels) is a comparatively recent commodity. Differentiation is what makes gold as a commodity different from gold as jewelry or coinage, for example, where there are particular features that may have particular appeal to the purchaser. In contrast, wheat of a particular grade is wheat, and so long as it is of the promised grade and quality, no one can be expected to care too much about anything apart from the actual physical amount available. That is what makes it a commodity.
As described in Section 7.2 of Clark, Lesourd and Thiéblemont (2001), one can categorise production systems into four various modes of production using Woodward’s classification, as described in Table 1.1.
Table 1.1 Woodward’s categorisation of production systems.
System Features Examples
Mass production Large scale production of an indivisible standardised product Automobile manufacturing
Process production Large scale production of a divisible standardised product Food, chemical manufacturing
Craft production Small scale production of a nonstandardised product Fashion
Project production Production of a unique product to bespoke client specifications Infrastructure construction (e.g. airports, bridges), building construction
From this we see that commodities are specifically outputs of process production, in that they are standardised (within various grades, typically) and divisible. Note that this has not always been the case, agriculture historically used to be more of a craft production enterprise. Commodities are generally tradeable goods, though there are some instruments that sometimes fall under the heading of commodity derivatives which are not, e.g. freight derivatives, weather derivatives, and other instruments that more closely resemble insurance products.
Within tradeable goods, there are some specific features of commodity markets within the sector of process production. Firstly, these goods generally have a long lead time for production (electricity generation being the notable exception) and generally have a liquid supply and demand market with reference pricing – this means that an equilibrium between supply and demand can in principle be found. In times when supply and demand are greatly out of line, generally inventories and storage come into play, as physical commodities can usually be warehoused subject to storage costs (electricity once again being an exception). This does, however, have the effect of increasing volatility both in historical terms and implied volatility (see Chapter 2) for ...

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