Financial Modelling in Commodity Markets

Viviana Fanelli

• Publisher: Chapman and Hall/CRC
• Year: 2020
• Print ISBN: 9781138739109
• eBook ISBN: 9781351730945
• Topic: Business
• Subtopic: Finance
• Index: Business

Financial Modelling in Commodity Markets provides a basic and self-contained introduction to the ideas underpinning financial modelling of products in commodity markets.

The book offers a concise and operational vision of the main models used to represent, assess and simulate real assets and financial positions related to the commodity markets. It discusses statistical and mathematical tools important for estimating, implementing and calibrating quantitative models used for pricing and trading commodity-linked products and for managing basic and complex portfolio risks.

Key features:

• Provides a step-by-step guide to the construction of pricing models, and for the applications of such models for the analysis of real data
• Written for scholars from a wide range of scientific fields, including economics and finance, mathematics, engineering and statistics, as well as for practitioners
• Illustrates some important pricing models using real data sets that will be commonly used in financial markets

Chapter 1

Commodity-linked Products

1.1Forward Contracts and Exchange Traded Futures

1.1.1Forward Price

1.1.2Futures Price

1.1.3Spot-forward Relationship

1.1.3.1Spot/Futures Arbitrage and the Basis

1.2Options

1.2.1European Options

1.2.2American Options

1.2.3Option Strategies

1.2.4Exotic Options

1.3Swaps

1.3.1Plain Vanilla Swap

1.3.2Other Swap Types

1.4Commodity Spreads

1.5Exercises

1.6Answers

1.1 Forward Contracts and Exchange Traded Futures

1.1.1 Forward Price

A forward contracts is a bilateral agreement to purchase or sell a certain amount of a commodity on a fixed future date at a predetermined contract price. The fixed future date is the delivery date of the commodity, and the predetermined contract price is the forward price. Thus, the participants of a forward contract on a commodity lock in a price today for future delivery. In Figure 1.1 we show the role of forward contract participants. The main characteristics of forward contracts are:

• They are over-the-counter (OTC) trades, executed through brokers.
• There are no cash flows until delivery.
• On delivery date the seller of the contract has the obligation to deliver the commodity in return for the forward price.
• A forward contract involves credit risk, where one of the counterparties does not, or cannot, fulfil his obligation to deliver or pay the commodity.

A forward contract can be mainly used for:

1. hedging the obligation to deliver or purchase a commodity at a future date;
2. guaranteeing a sales profit from a commodity production;
3. speculating on rising or falling commodity prices in case there is no liquid futures market.

FIGURE 1.1 Forward contract participants

Consider a customer who is long on forward contract for delivery date T at contract price K. The payoff at time T is given by the difference between the actual price S(T) of the underlying and the contract forward price K. It is illustrated in Figure 1.2.

FIGURE 1.2 The payoff at maturity of a forward contract

Let us assume that at an initial time 0 a customer sells a forward contract with delivery T and contract price K. The forward price will be F(0, T). We want to estimate the value of the contract, X(t), at a generic time t. In order to do this, at time t we sell another forward contract at the current market forward price F(t, T), so that the physical deliveries of both forward contracts in the portfolio cancel.

In fact, if we indicate with S(T) the market price of the underlying forward contract at delivery T, Table 1.1 illustrates the strategy payoff at every considered time.

TABLE 1.1: Forward contract strategy

	t	T
Long Forward at time 0	X(t)	S(T) − K
Short Forward at time t	0	F(t, T) − S(T)
Cash Flow	X(t)	F(t, T) − K

In order to avoid arbitrage possibilities, the fair value of a forward contract X(t) is uniquely given by

where r is the effective risk-free interest rate.

Example 1 Example of Fair Value.

An electricity producer buys 10,000t coal to be delivered at time T at a price K = 50 USD/t. At time t, the forward price for coal to be delivered at time T is F(t, T)...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Introduction
• 1. Commodity-linked Products
• 2. Spot Price Modelling
• 3. Forward Price Modelling
• 4. Derivative Valuation
• 5. Applications
• 6. Essential Statistics and Data Analysis
• Bibliography
• Index