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Energy Derivatives: Pricing and Risk Management

Les Clewlow & Chris Strickland with contributions from Vince Kaminiski, Grant Masson and Ronnie Chahal

This book (available in pdf form only), provides a comprehensive and technical treatment of the valuation and risk management of energy derivatives, within the oil, gas, and electricity markets.


Book outline

Energy markets around the world are rapidly being deregulated leading to unprecedented levels of competition in the energy industry, increased exposure to the prices on commodities, and exposing participants to potentially catastrophic risks.

This book provides a comprehensive and technical treatment of the valuation and risk management of energy derivatives, within the oil, gas, and electricity markets, and looks in depth at:

  • the behaviour of spot and forward prices
  • modelling and estimating volatility
  • structures that exist in the energy derivatives market and their applications
  • pricing and hedging of energy derivatives using single and multi-factor spot price models
  • using simulation and trinomial trees for pricing caps, floors, swaptions, and path-dependent securities such as barriers, Asians, lookbacks, and swing options.
  • multi-factor models of the forward curve, including volatility estimation and pricing of exotic derivatives
  • risk management of energy derivative positions
  • value-at-risk and credit risk for energy derivatives

A large proportion of the content is original research by the authors who have applied over 20 years combined derivatives experience and research in the energy markets.

Related Links

Corrections to the first edition (PDF format, 68kb)
Download Chapter 1 (PDF format, 422kb)

Chapter summaries

Chapter 1

In Chapter 1 we give an overview of the fundamental principles needed to model and price energy derivatives which will underpin the remainder of the book. In addition to introducing the techniques that underlie the Black-Scholes modelling framework we outline the numerical techniques of trinomial trees and Monte Carlo simulation for derivative pricing, which are used throughout the book.

Chapter 2

In Chapter 2 we discuss the analysis of spot energy prices. As well as analysing empirical price movements we propose a number of processes that can be used to model the prices. We look at the well-known process of Geometric Brownian Motion as well as mean reversion, stochastic volatility and jump processes, discussing each and showing how they can be simulated and their parameters estimated.

Chapter 3

Chapter 3, written by Vince Kaminski, Grant Masson and Ronnie Chahal of Enron Corp, discusses volatility estimation in energy commodity markets. This chapter builds on the previous one. It examines in detail the methods, merits and pitfalls of the volatility estimation process assuming different pricing models introduced in chapter 2. Examples from crude, gas and electricity markets are used to illustrate the technical and interpretative aspects of calculating volatility.

Chapter 4

Chapter 4 examines forward curves in the energy markets. Although such curves are well understood and straight-forward in most financial markets, the difficulty of storage in many energy markets leads to less well defined curves. In this chapter we describe forward price bounds for energy prices and the building of forward curves from market instruments. We outline the three main approaches which have been applied to building forward curves in energy markets: the arbitrage approach, the econometric approach, and deriving analytical values by modelling underlying stochastic factors.

Chapter 5

Chapter 5 presents an overview of structures found in the energy derivative markets and discusses their uses. Examples of products analysed in this chapter include a variety of swaps, caps, floors and collars, as well as energy swaptions, compound options, Asian options, barrier options, lookback options, and ladder options..

Chapter 6

Chapter 6 investigates single and multi-factor models of the energy spot price and the pricing of some standard energy derivatives. Closed form solutions for forward prices, forward volatilities, and European option prices both on the spot and forwards are derived and presented for all the models in this chapter including a three factor, stochastic convenience yield and interest rate model.

Chapter 7

Chapter 7 shows how the prices of path dependent and American style options can be evaluated for the models in Chapter 6. Simulation schemes are developed for the evaluation of European style options and applied to a variety of path dependent options. In order to price options which incorporate early exercise opportunities, a trinomial tree scheme is developed. This tree is built to be consistent with the observed forward curve and can be used to price exotic as well as standard European and American style options.

Chapter 8

Chapter 8 describes a methodology for valuing energy options based on modelling the whole of the market observed forward curve. The approach results in a multi-factor model that is able to realistically capture the evolution of a wide range of energy forward curves. The user defined volatility structures can be of an extremely general form. Closed-form solutions are developed for pricing standard European options, and efficient Monte Carlo schemes are presented for pricing exotic options. The chapter closes with a discussion of the valuation of American style options.

Chapter 9

Chapter 9 focuses on the risk management of energy derivative positions. In this chapter we discuss the management of price risk for institutions that trade options or other derivatives and who are then faced with the problem of managing the risk through time. We begin with delta hedging a portfolio containing derivatives and look at extensions to gamma hedging - illustrating the techniques using both spot and forward curve models. The general model presented in Chapter 8 is ideally suited to multi-factor hedging of a portfolio of energy derivatives and this is also discussed.

Chapter 10

Chapter 10 examines the key risk management concept of value-at-risk (VaR) applied to portfolios containing energy derivative products. After discussing the concept of the measure, we look at how the key inputs (volatilities, covariances, correlations, etc) can be estimated. We then compare the four major methodologies for computing VaR: Delta, Delta-gamma, historical simulation and Monte-Carlo simulation, applying each to the same portfolio of energy options. In this chapter we also look at testing the VaR estimates for various underlying energy market variables.

Chapter 11

Finally, in Chapter 11 we review modelling approaches to credit risk. We look in detail at two quite different approaches, CreditMetrics (J. P. Morgan (1997)) and CreditRisk+ (Credit Suisse Financial Products (1997)) for which detailed information is publicly available. Together these provide an extensive set of tools with which to measure credit risk. We present numerical examples of applying these techniques to energy derivatives.

About the authors

Les Clewlow and Chris Strickland – are the founding directors of Lacima Group through which they provide software, consulting and training services for energy risk management, valuation and optimisation. They are the authors of the book “Implementing Derivatives Models” (Wiley, 1998) and editors of “Exotic Options: The State of the Art” (ITP, 1998) and have published many articles in both academic and trade journals. They also hold Associate Research Positions at the University of Technology, Sydney and the University of Warwick, UK. Les and Chris received their Ph.D.s in Computer Science and Finance, respectively, from the University of Warwick.

Vincent (Vince) Kaminski – was Managing Director and Head of Research for Enron Corp, which he joined in June 1992. Previously, Vince was a Vice President in the research department of Salomon Brothers in New York and a manager in AT&T Communications in Bedminster, New Jersey. Vince is a recipient of the 1999 James H. McGraw Award for Energy Risk Management (Energy Risk Manager of the Year). Vince holds an M.S. degree in international economics and a Ph.D. degree in mathematical economics from the Main School of Planning and Statistics in Warsaw, Poland, and an MBA from Fordham University in New York.

Grant Masson – was a vice president with the research group of Enron Corp. He oversaw the quantitative support for asset and derivative structure valuations and market analysis for both domestic and international electricity trading and origination. Prior to joining Enron in 1994, Grant spent five years at the University of Basel as a research scientist specialising in experimental nuclear physics. He received a BA from Rice University in Houston and MS and Ph.D. degrees in physics from the University of Wisconsin — Madison.

Ronnie Chahal – was a manager in the Enron Research group and provided analytical support to the risk management group in Enron Energy Services. He has a Ph.D. in Finance from Georgia State University, Atlanta, Georgia.

What the experts say

…a thorough and comprehensive overview of energy derivatives markets, instruments, derivatives pricing and risk management methodologies…This is the first book that explains, in detail, energy price behavior and the different modeling approaches employed to capture the complex realities of these markets. This book should become a reference for energy derivatives traders, risk managers, energy risk consultants, and anyone else interested in the fascinating area of energy derivatives.

Mark Garman. Professor Emeritus of Finance, Walter A. Haas School of Business Administration, at University of California, Berkeley, CEO of Financial Engineering Associates, Inc.

This book provides an excellent overview of the practical quantitative tools that are used in modern energy risk modelling and management. It combines solid academic rigor with the practical experience that comes from working closely with companies in the energy field.

Corwin Joy, PhD, Vice President Financial Models, Caminus

The book gives a clear, comprehensive and well presented description of the exciting new world of energy derivatives. The book superbly achieves its goal of acquainting the reader with the advanced methods used to price complex energy derivative products. The book also gives an excellent introduction to the energy markets, focusing on their unique properties and presenting an overview of energy products, which may be very useful to a general reader, as sometimes these products have no parallel in more familiar financial markets. The chapter on value-at-risk is also very helpful, because it addresses rather special challenges faced by anyone managing risks of energy derivatives. The book has a large number of interesting and well thought-out examples which significantly simplify the task of understanding difficult model implementation issues. Undoubtedly, the book will become an indispensable reference source for risk managers, researchers and practitioners interested in understanding complex issues arising in modeling energy markets, and in learning modern techniques for valuing energy derivatives.

Alexander Eydeland, Vice President, Head of Research, Southern Energy Americas Group

A comprehensive introduction to modelling energy derivatives. The book provides an excellent summary of equilibrium and no-arbitrage pricing models emphasising numerical methods and their practical implementation.

Ilia Bouchouev, PhD, Vice President of Structured Products and Derivatives Trading at Koch Petroleum Group

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