EC2137 : Derivatives
Dr. Gaurav Mehta
Lecture 1
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Module Outline &Contacts
 Module leader: Dr Gaurav Mehta
• Office: Brookfield, 2.06.
• Office Hours: Tuesday, 1:30pm-3:30pm (Appointment)
• Email: gm360@leicester.ac.uk
 Lectures: In total 10 two-hour lectures.
Seminars: Weekly from a week after next week. In total 5 seminars*.
•In seminar groups you will discuss and solve problem sets.
 Mid Term Test (MCQs): 20% and Final Examination (On Campus): 80%
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Module Contents
Lecture 1, Week 26
What is a futures/forward contract? What are the mechanics
of futures markets?
Lecture 2, Week 27
Types of traders
Hedging strategies using futures and forwards
Lecture 3, Week 28
Derivation of the optimal hedge ratio
Lecture 4, Week 29
Stock Index futures
Lecture 5, Week 30
How do we price futures and forward contracts?
Lecture 6, Week 32
Pricing of futures on stock indexes. Forwards and futures on
currencies. Futures prices and expected future spot prices.
Lecture 7, Week 33
Interest rate futures
Lecture 8, Week 34
Introduction to Swaps
Lecture 9, Week 35
Introduction to Options
Lecture 10, Week 36
Revision of module material and going through the Mock
exam
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Textbook
John C. Hull (2017) Fundamentals
of Futures and Options Markets, 9th edition.
(other editions are also fine).
 The book and the table of contents can be
accessed via reading lists for EC2137.
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This lecture:
 Introduction to derivatives.
 Futures markets and futures exchanges.
 Mechanics of the futures markets.
 Characteristics of futures and forwards contracts.
Reading:
Hull, CH1 (pages 1-10) and CH2.
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1. The Nature of Derivatives
Derivatives play a key role
in transferring risks in the
economy.
A derivative is an instrument, whose value depends on the
values of other more basic underlying assets (e.g., a stock,
index, commodity, interest bearing assets, etc.).
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Examples of Derivatives
o Futures Contract
o Forward Contract
o Swaps
o Options
We will focus in this module on Futures and Forward contracts, as well
as become familiar with Swaps and Options.
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Examples of Derivatives
Futures Contract: an agreement to buy or sell an asset at a certain
time in the future for a certain price.
Forward Contract: like a futures contract but traded in the Over
the Counter markets (OTC).*
Swap: an agreement between two parties to exchange cash flows
at some time points in the future. Swaps are also OTC traded.
Options: gives the holder the right to buy/ sell an asset at a certain
price by a certain date.
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2. Futures Contracts
• A futures contract is an agreement to buy or sell an asset at
a certain time in the future for a certain price.
 By contrast in a spot contract there is an agreement to buy
or sell the asset immediately (or within a very short period).
• The futures prices for a particular contract is the price at
which you agree to buy or sell at a future time.
•It is determined by the supply and demand in the same way
as a spot price.
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Futures: some examples
One can trade futures contracts
on most types of assets from:
• commodities (sugar, grains, orange juice,
oil, etc.) to
• financial instruments, such as equities,
bonds and indexes.
• Some new types of futures contracts are
constantly introduced by the exchanges.
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Convergence of Futures to Spot
(Figure 2.1, page 28, Hull)
• As the delivery period for a
futures contract is approaching, the
futures price converges to the
spot price of the underlying asset.
Futures
Price
Spot Price
•
Time
When the delivery period is
reached, the futures price is equal
to (or is very close to) the spot price
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Terminology
The party that has agreed to buy has a long
position
The party that has agreed to sell has a short
position
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Examples of Futures Contracts
Agreement to:
◦buy 100 oz. of gold @ US$2750/oz. in
February
◦sell £62,500 @ 1.2500 US$/£ in March
◦sell 1,000 bbl. of oil @ US$85/bbl. in April
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Example of entering into a futures contract
It is June and you want to buy 5000 bushels of corn for September delivery. -> You contact your broker and
he/she places a bid to the CME group*.
Another trader makes an offer to sell 5000 bushels of corn for September delivery.
The bid and the offer are matched by your brokers and a price is determined via laws of supply and demand.
Suppose you make a bid to buy at 600 cents per bushel and the other trader offers to sell 625 cents per
bushel. If the demand is less than the total offers for sale. Then the trade may be executed close to 600 cents
per bushel.
You hold a long position in the futures contract. The other trader (the seller of the corn) holds a short
position in the futures contract.
Note: Futures contract is a binding contract for both parties.
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Another Example
January: an investor enters a long futures contract to buy
100 oz of gold @ $2,750 per oz in April
April: the price of gold is $2,825 per oz
What is the investor’s profit or loss here in
April?
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Answer
The profit is:
(2,825- 2,750) * 100 = $ 7,500 [this is for 1 futures contract]
since the long futures contract secured you a cheaper gold
price than the actual spot price in that month.
Note: we make here a simplifying assumption that gold would have been delivered to the long
position holder in April (this is usually not the case in futures contracts, as we will discuss
later).
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3. Exchanges Trading Futures
 CME Group (Chicago Mercantile Exchange (CME); New York
Mercantile Exchange (NYMEX); Chicago Board of Trade (CBOT).
 Intercontinental Exchange:
- NYSE Euronext
- in UK: London International Financial Futures Exchange (LIFFE)
and many more (see list at end of the Hull book on p.581).
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Electronic Trading
o Traditionally futures contracts have been traded using the open outcry
system, where traders physically meet on the floor of the exchange.
oThis has now been largely replaced by electronic trading and high
frequency algorithmic trading is becoming an increasingly important
part of the market
See e.g.: Financial Times (2016)
‘CME calls time on New York open
outcry options floor’
https://www.ft.com/content/33141038-01b9-11e6-99cb83242733f755
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Some emerging futures
contracts – some FT news
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Main characteristics of futures
contracts
1. exchange traded (traded on official exchanges)
2. standardized (delivery, contract size, price, type of asset strictly specified).
3. settled daily (‘marking to market’) This to reflect the gains/losses as the futures prices change on
daily basis.
4. delivery often does NOT take place* Futures contracts are usually “closed out” before maturity,
i.e., the physical delivery of the asset does not take place.
5. Counterparty risk is almost non-existent (due to point 3). This is the risk of the short or long
position holder not being able to fulfil his obligation and cover possible losses in the futures contract.
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4. Mechanics of futures markets:
margins and daily settlement.
 We mentioned that futures contracts are Exchange traded
 An important aspect is that futures contracts are settled
daily
 To reduce the risk of counterparty walking away (credit
risk) the so-called margins are introduced.
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Margin
A margin is cash or
marketable
securities
deposited by an
investor with his or
her broker.
The balance in
the margin
account is
adjusted to reflect
daily settlement.
Margin minimizes
the possibility of a
loss through a
default on a
contract.
We will do an
example to
define some
different types of
margins:
- Initial margin.
- Maintenance
margin.
- Variation
margin and
`Margin Call’
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Example of daily settlement and types of margins
1) On June the 5th you contact your broker to go long on 2 (two)
December gold futures on NYMEX.
This is the price
2) Price of futures, when you enter the contract is: $ 400/oz
of December
futures.
3) We assume the size of each contract: 100 oz
4) When entering the contract you place funds (initial margin) into your
margin account.
5) Initial margin = $ 2000/contract. Hence, in total: $ 4000 to be
deposited.
6) Each trading day the margin account is adjusted to reflect the gains/
losses of each party in respect to the daily settlement price (so called
‘marking to market’).
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Marking to market is
taking place at the
end of each trading
day.
Cont.
7) Suppose by the end of June 5 the futures price drops to $ 397/oz.
8) As a holder of the long position you make a loss in respect to original
price: -3(100*2)= -$600.
9) The balance on your margin account is reduced from: $ 4000-> $3400.
The reduction goes via the exchange to the account of the short position
holder.
10) Now, suppose that by the end of June 5th and the futures price
instead raises to $ 403/oz.
11) There is a gain: 3(200)= $600
12) The balance on the margin account is augmented from $ 4000->
$4600. This money comes from the margin account of the trader with a
short position.
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Cont.
Final points:
13) Any balance over and above the initial margin can be withdrawn.
14) To avoid the balance in the margin account from becoming
negative, a so called maintenance margin is introduced (which is lower
than the initial margin).
15) If the amount in the margin account falls below the maintenance
margin, then you receive a so called ‘margin call.
16) This means that you are asked by the broker to top up until you
reach the initial margin latest by next day.
17) These extra deposited funds are known as the variation margin.
18) If these funds are not provided, the broker closes the position
immediately.
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Margin Cash Flows When Futures
Price Decreases
Benefits the short
position holder, as the
long position holder paid a
higher price when entering
the contract.
Is making losses
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Margin Cash Flows When Futures Price
Increases
Benefits the long position
holder, as the short
position holder secured a
too cheap selling price
when entering the contract.
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Another example of a futures
trade (for your own consideration)
(page 29-30 in Hull)
An investor takes a long position on 2 December gold
futures contracts on June 5
◦ contract size is 100 oz.
◦ futures price is US$1650/ oz.
◦ initial margin requirement is US$6,000/contract
(US$12,000 in total)
◦ maintenance margin is US$4,500/contract (US$ 9,000
in total)
Lower than
initial margin
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A Possible Outcome (Table 2.1, page 30)
Day
Trade
Price ($)
1
1,650.00
Settle
Price ($)
Daily
Gain ($)
Cumul.
Gain ($)
Margin
Balance ($)
12,000
1
1,641.00
−1,800
− 1,800
10,200
2
1,638.30
−540
−2,340
9,660
…..
…..
…..
……
6
1,636.20
−780
−2,760
9,240
7
1,629.90
−1,260
−4,020
7,980
8
1,630.80
180
−3,840
12,180
…..
…..
…..
……
780
−4,620
15,180
…..
…..
16
1,626.90
Margin
Call ($)
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4,020
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5. Forward Contracts
• Forward contracts are similar to futures, except that they
trade in the over-the-counter markets (OTC).
• Forward contracts are popular on currencies (to hedge
currency risk) , interest rates and fixed income securities.
There is no daily
settlement, but
counterparty might
require collateral
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Over-the Counter Markets (OTC)
•The over-the counter market is an important alternative to
exchanges
•Trades are usually between financial institutions, corporate
treasurers, and fund managers
•Transactions are much larger than in the exchange-traded
market
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Size of OTC and Exchange-Traded Markets
(Figure 1.2, Page 6)
Source: Bank for International Settlements.
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Bilateral Clearing vs. Central
Clearing House
Individual
traders
Bilateral clearing
(OTC markets)
Central clearing
(Exchange trading)
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Example Forward contract: Foreign Exchange Quotes for
USD/GBP exchange rate on June 22, 2012 (See Table 1.1, page
7)
Spot
Bid (buy £)
1.5585
Offer (sell £)
1.5589
1-month forward
1.5582
1.5587
3-month forward
1.5579
1.5585
6-month forward
1.5573
1.5580
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Simple example of currency forward
You are a treasurer of a US company and you have to pay 1M
pounds in 6 months.
How can you hedge against the currency fluctuations?
(we use a forward with exchange rate of 1.5 USD/GBP in this
example).
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Simple example of currency forward
1) You are a treasurer of a US company and you have to pay 1M pounds
in 6 months.
How can you hedge against the currency fluctuations?
2) You enter a long forward (i.e., to buy pounds) for delivery in 6
months.
3) The bank is willing to sell (offer rate) 1.5 USD/GBP. The bank has a short
forward position.
4) In 6 months you pay the $ 1.5 M and the bank ‘delivers’ the £ 1M.
5) If e.g., the actual spot rate in 6 months rises to 1.7 USD/GBP you make a
profit (200 000 USD)
6) If the actual spot rate in 6 months drops to 1.3 USD/GBP you make a loss
to the corporation (- 200 000 USD).
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Characteristics of the Forward Contracts
1. Private contracts with parties (not exchange traded)
2. Non standardized (tailor-made agreement between two parties like a
corporation and a bank)
3. Settled at the end of Contract
4. Delivery often takes place (as in previous example the bank actually
‘delivers’ the pounds)
Counterparty risk is existent (due to points 1-3). This means that the
counterparty might not fulfil the obligations at maturity of the contract.
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Futures vs. Forwards: summary
of differences
The key difference:
 Forward contracts are customised agreements between 2 parties
and so traded over-the-counter (OTC).
 Future contracts are standardised contracts traded on an
exchange.
Since forwards contracts are determined by the parties involved,
the parties may agree:
– A contract on any underlying asset – Any date for the transaction
– Any quantity they desire
– Special provisions
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Key differences (cont.)
 In contrast, to allow futures contracts to be traded on an exchange they
must be standardised.
o Only pre-specified delivery dates
o Only certain assets
o Specified terms of delivery
 A consequence of futures being exchange traded and the central
clearing procedure:
o Futures are much more liquid.
o Since the future contract is bought/sold from the exchange it may be
“closed” at any time a trader wants.
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Final Points About Futures
•They are settled daily (‘marking to market’).
•Closing out a futures position involves entering an offsetting
trade (i.e., if you hold a long position, you short the same
number of contracts for the same delivery date).
•Most contracts are closed out before maturity.
•If a futures contract is not closed out before maturity, it is
usually settled by delivering the assets underlying the
contract.
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