Derivatives Markets

Lecture 3: PLAIN DERIVATIVES, cont.

Rafał Łochowski Spring 2011 Term structure of

• – it is the situation where, and the amount by which, the price of a commodity for future delivery is higher than the spot price , or a far future delivery price higher than a nearer future delivery. – Example: a forward oil contract for twelve months in the future is selling for $100 today, while today's spot price is $75. The expected spot price twelve months in the future may actually still be $75. Contango, cont.

• To purchase a contract at more than $75 supposes a loss of $25 to the agent who "bought forward" as opposed to waiting a year to buy at the spot price when oil is actually needed. • Experience tells major end users of commodities that spot prices are unpredictable. Locking in a future price puts the purchaser "first in line" for delivery even though the contract will, as it matures, converge on the spot price. Contango, cont.

• Sellers like to "sell forward" because it locks in an income stream. Farmers are the classic example: by selling their crop forward when it is still in the ground they can lock in a price, and therefore an income, which helps them qualify, in the present, for credit. • A contango is normal for a non-perishable commodity which has a cost of carry. Such costs include warehousing fees and interest forgone on money tied up, less income from leasing out the commodity if possible ( e.g. gold). Contango cont.

• For perishable commodities, price differences between near and far delivery are not a contango. Different delivery dates are in effect entirely different commodities in this case, since fresh eggs today will not still be fresh in 6 months' time, 90 -day treasury bills will have matured, etc. • The contango should not exceed the cost of carry, because producers and consumers can compare the futures contract price against the spot price plus storage, and choose the better one. Arbitrageurs can sell one and buy the other for a theoretically risk-free profit.

• Backwardation – is the name for the condition that the market quotes a lower price for a more distant delivery date, and a higher price for a nearby delivery date. • It is argued that backwardation is abnormal, and suggests supply insufficiencies in the corresponding (physical) spot market. However, many commodities markets are frequently in backwardation, especially when the seasonal aspect is taken into consideration, e.g. perishable and/or soft commodities. Rational pricing of futures contracts • In a futures contract, for no to be possible, the price paid on delivery (the ) must be the same as the cost (including interest) of buying and storing the asset. • We will use the following notation T - time until delivery date (in years) S F - prices of the asset underlying the forward 0, 0 contract and futures price respectively r - (zero-coupon) risk free interest rate per annum Material from J. Hull’s book

• For this part of the lecture please download slides for sixth edition of J. Hull’s book Options, Futures, and Other Derivatives, from the web page http://www.rotman.utoronto.ca/~hull/ofodslides/ • After downloading and unzipping the slides go to the presentations CH05HullOFOD6thEd.ppt and CH07HullOFOD6thEd.ppt Eurodollar Futures

• A Eurodollar is a dollar deposited in an US bank or bank outside the United States • Eurodollar futures are futures on the 3-month Eurodollar deposit rate (same as 3 -month LIBOR rate) • One contract is on the rate earned on $1 million • If Q is the quoted price of a Eurodollar futures contract, the value of one contract is 10,000[100-0.25(100-Q)] Eurodollar Futures cont.

• A change of one basis point or 0.01 in a Eurodollar futures quote corresponds to a contract price change of $25 • A Eurodollar futures contract is settled in cash • When it expires (on the third Wednesday of the delivery month) the final settlement price is 100 minus the actual three month deposit rate Example

• Suppose you buy (take a long position in) a contract on November 1 • The contract expires on December 21 • The prices are as shown • How much do you gain or lose a) on the first day, b) on the second day, c) over the whole time until expiration? Example cont.

Date Quote Nov 1 97.12 Nov 2 97.23 Nov 3 96.98 ……. …… Dec 21 97.42

Options, Futures, and Other Derivatives 6th 6.12 Edition, Copyright © John C. Hull 2005 Example cont.

• If on Nov. 1 you know that you will have $1 million to invest on for three months on Dec 21, the contract locks in a rate of 100 - 97.12 = 2.88% • In the example you earn 100 – 97.42 = 2.58% on $1 million for three months (=$6,450) and make a gain day by day on the futures contract of 30 ×$25 =$750 Forward Rates and Eurodollar Futures • Eurodollar futures contracts last as long as 10 years • For Eurodollar futures lasting beyond two years we cannot assume that the forward rate equals the futures rate Forward Rates and Eurodollar Futures cont. • Futures is settled daily where forward is settled once • Futures is settled at the beginning of the underlying three -month period; forward is settled at the end of the underlying three- month period