Chapter One
An Introduction to Derivative Products
SYNOPSIS The purpose of this chapter is to outline the main features of derivatives and provide a description of the main ways in which they are priced and valued.
This chapter is divided into two distinct sections that cover:
The key features of the derivative "building block" products
The principles of how each of the products is priced and valued.
The coverage is not particularly mathematical in style, although numerical examples are included where it helps to illustrate the key principles.
In the first section the fundamental concepts of the main derivative products are considered. The products covered include:
Futures
Forwards
Swaps
Options (mostly "vanilla" with some "exotic" coverage)
In the second section the focus is on the pricing of derivatives. The approach considers that all of the building block markets are linked through mathematical relationships and describes how the price of one product can be derived from another.
One of the unique elements of pricing commodity derivatives is the existence of the convenience yield, which is explained in conjunction with the concepts of contango and backwardation.
Two extra themes are developed in the pricing section that are relevant to other parts of the book. The first is a discussion on put-call parity, which will help the reader to understand how some structures are created. This idea is then developed to outline the potential sources of value in risk management solutions.
The chapter concludes with a description of the main measures of option risk management - the Greeks.
When analysing derivatives it is convenient to classify them into three main building blocks:
Forwards and futures
Swaps
Options.
However, within the option category it is possible to make a distinction between two sub-categories, the so-called "plain vanilla" structures (that is, options that conform to a basic accepted profile) and those that are considered "exotic", such as binaries and barriers.
For ease of illustration we will use gold in the following examples.
1.1 FORWARDS AND FUTURES
A forward contract will fix the price today for delivery of an asset in the future. Gold sold for spot value will involve the exchange of cash for the metal in two days'' time. However, if the transaction required the delivery in say 1 month''s time it would be classified as a forward transaction. Forward contracts are negotiated bilaterally between the buyer and the seller and are often characterised as being "over the counter".
The forward transaction represents a contractual commitment; so if gold is bought forward at, say, USD 430.00 an ounce but the price of gold in the spot market is only USD 420.00 at the point of delivery, I cannot walk away from the forward contract and try to buy it in the underlying market. However, it is not impossible to terminate the contract early. This could be achieved by agreeing a "break" amount, which would reflect the current economic value of the contract.
A futures contract is traded on an organised exchange with the New York Mercantile Exchange being one example. Economically a future achieves the same result as a forward by offering price certainty for a period in the future. However, the key difference between the contracts is in how they are traded. The contracts are uniform in their trading size, which is set by the exchange. For example, the main features of the contract specification for the gold future are listed in Table 1.1.
There are some fundamental differences between commodity and financial products traded on an exchange basis. One of the key differences is that futures require collateral to be deposited when a trade is executed (known as initial margin). Although different exchanges will work in different ways, the remittance of profits and losses may take place on an ongoing basis (variation margin) rather than at the maturity of the contract. An example of this is detailed in the chapter on base metals.
Settlement of financial futures is often for a single date specified by the exchange, such as the third Wednesday in March, June, September or December. For commodity futures settlement could be for any day within the ensuing three months (see "trading days" section in the above specification). By offering delivery on any day for the current and two successive months, this commodity future possess a feature of the forward market - the flexibility to settle for a variety of dates. Another difference is the concept of grade and quality specification. If one is delivering a currency, the underlying asset is homogeneous - a dollar is always a dollar. However, because metals have different shapes, grades and quality, there must be an element of standardisation to ensure that the buyer knows what he or she is receiving. Some of the criteria that NYMEX apply include:
The seller must deliver 100 troy ounces (?5%) of refined gold.
The gold must be of a fineness of no less than 0.995%.
It must be cast either in one bar or in three 1-kilogram bars.
The gold must bear a serial number and identifying stamp of a refiner approved and listed by the Exchange.
1.2 SWAPS
In a swap transaction two parties agree to exchange cashflows, the sizes of which are based on different price indices. Typically, this is represented as an agreed fixed rate against a variable or floating rate. Swaps are traded on an agreed notional amount, which is not exchanged but establishes the magnitude of the fixed and floating cashflows. Swap contracts are typically of longer-term maturity (i.e. greater than one year) but the exact terms of the contract will be open to negotiation. For example, in many base metal markets a swap transaction is often nothing more than a single period forward, which allows for the transaction to be cash settled, involving the payment of the agreed forward price against the spot price at expiry.
The exact form may vary between markets, with the following merely a sample of how they may be applied in a variety of different commodity markets.
Gold: Pay fixed lease rate vs receive variable lease rate.
Base metals: Pay fixed aluminium price vs receive average price of near dated aluminium future.
Oil: Pay fixed West Texas Intermediate (WTI) price vs receive average price of near dated WTI future.
Swaps will usually start as spot and so become effective two days after they are traded. However, it is also possible for the swap to become effective at some time in the future - a forward starting swap. The frequency with which the cashflows are settled is open to negotiation but they could vary in tenor between 1 month and 12 months. Where the payments coincide there is a net settlement between the two parties. One of the features of commodity swaps that is not shared by financial swaps is the use of an average rate for the floating leg. This is because many of the underlying exposures that commodity swaps are designed to hedge will be based on some form of average price.
The motivation for entering into a swap will differ between counterparties. For a corporate entity one of their main concerns is risk transference. Consider a company that has to purchase a particular commodity at the market price at regular periods in the future. To offset the risk that the underlying price may rise, the company would receive a cashflow under the swap based on movements in the market price of the commodity and pay a fixed rate. If the counterparty to the transaction were an investment bank, the latter would now have the original exposure faced by the corporate. The investment bank would be receiving a fixed rate and paying a variable rate, leaving it exposed to a rise in the price of the underlying commodity. In turn the investment bank will attempt to mitigate this exposure by entering into some form of offsetting transaction. The simplest form of this offsetting deal would be an equal and opposite swap transaction. In order to ensure that the bank makes some money from this second transaction, the amount it receives from the corporate should offset the amount paid to the offsetting swap counterparty.
Swaps are typically traded on a bid-offer spread basis. From a market maker''s perspective (that is the institution actually giving the quote) the trades are quoted as follows:
Bid Offer
Pay fixed Receive fixed Receive floating Pay floating Buy Sell Long Short
Although the terms "buy" and "sell" are often used in swap quotes the actual meaning is often confusing to anyone looking at the market for a first time. The convention in all swap markets is that the buyer is receiving a stream of variable cashflows for which the price is a single fixed rate. Selling a swap requires the delivery of a stream of floating cashflows for which the compensation is a single fixed rate.
1.3 OPTIONS
A forward contract offers price certainty to both counterparties. However, the buyer of a forward is locked into paying a fixed price for a particular commodity. This transaction will be valuable if the price of the commodity subsequently rises, but will be unprofitable in the event of a fall in price. An option contract offers the best of both worlds. It will offer the buyer of the contract protection if the price of the underlying moves against him but allows him to walk away from the deal if the underlying price moves in his favour.
This leads to the definition of an option as the right but not the obligation to either buy or sell an underlying commodity at some time in the future at a price agreed today. An option that allows the holder to buy the underlying asset is referred to as a call. Having the right to sell something is referred to as a put. Options may be either physically settled (that is the commodity is actually delivered/received) or cash settled. The price at which the underlying is traded if the option is exercised is referred to as the strike price. The strike price is negotiated between the option buyer and seller. Cash settlement involves the seller paying the buyer the difference between the strike and the spot price at the point of exercise. Cash settlement is advantageous to the buyer as it may be more convenient to either source or deliver the commodity separately; the option would simply offer price protection.
Options come in a variety of styles relating to when the holder can actually exercise his right. A European style option allows the holder to exercise the option only on the final maturity date. An American style option allows the holder to exercise the option at any time prior to final maturity. A Bermudan option allows the holder to exercise the option on a pre-agreed set of dates prior to maturity.
An option that is "in-the-money" (ITM) describes a situation where it would be more advantageous to trade at the strike price rather than the underlying market price. Take for example an American style option to buy gold at USD 400 an ounce when the current spot price is, say, USD 425; the option to buy at the strike is more attractive than the current market price. Where the option is "out-of-the-money" (OTM) the strike is less attractive than the market price. If the same American style option had a strike rate of USD 430 the higher strike makes the option less attractive than being able to buy the underlying at a price of USD 420. Finally an option where the strike is equal to the current market price is referred to as being "at-the money" (ATM).
Since options confer rights to the holder a premium is payable by the buyer. Typically this is paid up front but certain option structures are constructed to be zero premium or may involve deferment of the premium to a later date. Premiums on options are quoted in the same units as the underlying asset. So since physical gold is quoted in dollars per troy ounce, the premium will be quoted in the same manner.
Many of the derivatives strategies based on options that are discussed and illustrated within the text are based on the value of the option at maturity. These are presented in Figure 1.1.
In the top left-hand part of Figure 1.1, the purchase of a call option is illustrated. If, at expiry of the option, the market price is lower than the strike, the option is not exercised and the buyer loses the premium paid. If the underlying price is higher than the strike price the option is exercised and the buyer receives the underlying asset (or its cash equivalent), which is now worth more in the underlying market than the price paid (i.e. the strike price). This profit profile is shown to the right of the strike price. On the other side of the transaction there is the seller of a call option (top right-hand quadrant of Figure 1.1). The profit and loss profile of the seller must be the mirror of that of the buyer. So in the case of the call option the seller will keep the premium if the underlying price is less than the strike price but will face increasing losses as the underlying market price rises.
The purchase of a put option is illustrated in the bottom left-hand quadrant of Figure 1.1. Since this type of option allows the buyer to sell the underlying asset at a given strike price, this option will only be exercised if the underlying price falls. If the underlying price rises, the buyer loses the premium paid. Again the selling profile for the put is the mirror image of that faced by the buyer. That is, if the underlying price falls, the seller will be faced with increasing losses but will keep the premium if the market price rises.
Exotic options are a separate class of options where the profit and losses at exercise do not correspond to the plain vanilla American/European styles. Although there is a proliferation of different types of exotic options (many of which will be introduced in the main text), it is worth introducing two key building blocks, which feature prominently in derivative structures.
A binary option (sometimes referred to as a "digital") is very similar to a simple bet. The buyer pays a premium and agrees to receive a fixed return. Very often the strike rate on the digital is referred to (somewhat confusingly) as a "barrier". With a European style call option the holder will deliver the strike price to the seller and receive a fixed amount of gold. However, the value of the gold will depend on where the value of gold is trading in the spot market upon exercise. With a binary option the buyer will receive a fixed sum of money if the option is exercised irrespective of the final spot level.
The purchaser of a barrier option will: (1) start with a conventional "plain vanilla" option that could subsequently be cancelled prior to maturity (known as a "knock-out"), or (2) start with nothing and be granted a plain vanilla option prior to the maturity of the transaction (known as a "knock-in").
The cancellation or granting of the option will be conditional upon the spot level in the underlying market reaching a certain level, referred to either as a "barrier" or a "trigger".
The position of the barrier could either be placed in the out-of-the-money region or in the in-the-money region. This will be above or below the current spot price, as we will show below. The former are referred to as "standard" barriers with the later known as "reverse" barriers. This could result in what may initially seem like a bewildering array of possibilities, and Figure 1.2 summarises the concepts.
To illustrate the concept further, let us return to the option example illustrated earlier and concentrate on analysing a call option. We will assume that the option is out-of-the-money and the current market conditions exist:
Spot USD 425 Strike USD 430 Maturity 3 months
(Continues...)
Excerpted from Commodity Derivativesby Neil C. Schofield Copyright © 2007 by Neil C. Schofield. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
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