Lecture 1: Introduction

1

Gwion Williams

ASB4417/4817 Financial Engineering

What is a Derivative?

A derivative is an instrument whose value

depends on, or is derived from, the value

of another asset.

Examples: futures, forwards, swaps,

options, exotics

2

Why Derivatives Are Important

Derivatives play a key role in transferring risks in the

economy

The underlying assets include stocks, currencies,

interest rates, commodities, debt instruments,

electricity, insurance payouts, the weather, etc

Many financial transactions have embedded

derivatives

The real options approach to assessing capital

investment decisions has become widely accepted

3

How Derivatives Are Traded

On exchanges such as the Chicago Board

Options Exchange

In the over-the-counter (OTC) market

where traders working for banks, fund

managers and corporate treasurers

contact each other directly

4

Size of OTC and Exchange-Traded Markets

5

Source: Bank for International Settlements. Chart shows total principal amounts for

OTC market and value of underlying assets for exchange market

The Lehman Bankruptcy

Lehmans filed for bankruptcy on September 15, 2008.

This was the biggest bankruptcy in US history

Lehman was an active participant in the OTC derivatives

markets and got into financial difficulties because it took

high risks and found it was unable to roll over its short

term funding

It had hundreds of thousands of transactions

outstanding with about 8,000 counterparties

Unwinding these transactions has been challenging for

both the Lehman liquidators and their counterparties

6

How Derivatives are Used

To hedge risks

To speculate (take a view on the future direction of

the market)

To lock in an arbitrage profit

To change the nature of a liability

To change the nature of an investment without

incurring the costs of selling one portfolio and

buying another

7

Foreign Exchange Quotes for GBP, May 24, 2010

8

Bid Offer

Spot 1.4407 1.4411

1-month forward 1.4408 1.4413

3-month forward 1.4410 1.4415

6-month forward 1.4416 1.4422

Forward Price

The forward price for a contract is the

delivery price that would be applicable to

the contract if were negotiated today (i.e., it

is the delivery price that would make the

contract worth exactly zero)

The forward price may be different for

contracts of different maturities (as shown

by the table)

9

Terminology

The party that has agreed to buy has what is termed a long position

The party that has agreed to sell has what is termed a short position

10

Class Exercise

On May 24, 2010 the treasurer of a corporation enters

into a long forward contract to buy 1 million in six

months at an exchange rate of 1.4422

This obligates the corporation to pay $1,442,200 for 1

million on November 24, 2010

What are the possible outcomes?

HINT consider different market conditions in 6 months

11

Profit from a Long Forward Position (K= delivery price=forward price at time contract is

entered into)

12

Profit

Price of Underlying at

Maturity, ST K

Profit from a Short Forward Position (K= delivery price=forward price at time contract is entered

into)

13

Profit

Price of Underlying

at Maturity, ST K

Futures Contracts

Agreement to buy or sell an asset for a

certain price at a certain time

Similar to forward contract

Whereas a forward contract is traded OTC,

a futures contract is traded on an exchange

Less risk involved compared to forwards:

exchange traded means guarantee of

contract being honored

14

Exchanges Trading Futures

CME Group (formerly Chicago Mercantile

Exchange and Chicago Board of Trade)

NYSE Euronext

BM&F (Sao Paulo, Brazil)

TIFFE (Tokyo)

and many more (see list at end of book)

15

Types of underlying assets in futures contracts

Commodities:

Pork bellies, live cattle, sugar, wool, copper, gold, oil.

Financial assets:

Stock indices, currencies and Treasury bonds

16

Examples of Futures Contracts

Agreement to:

Buy 100 oz. of gold @ US$1400/oz. in

December

Sell 62,500 @ 1.4500 US$/ in March

Sell 1,000 bbl. of oil @ US$90/bbl. in

April

17

Class Exercise 2 Gold: An Arbitrage Opportunity?

Suppose that:

The spot price of gold is US$1,400

The 1-year quoted futures price of gold is US$1,500

The 1-year US$ interest rate is 5% per annum

Is there an arbitrage opportunity?

18

Gold: Another Arbitrage Opportunity?

Suppose that:

- The spot price of gold is US$1,400 - The 1-year quoted futures price of gold is

US$1,400

- The 1-year US$ interest rate is 5% per annum

Is there an arbitrage opportunity?

19

2. Gold: Another Arbitrage Opportunity?

Sell short gold at spot of $1,400

Invest $1,400 at 5% for 1 year = $1,470

Enter long into futures contract to buy back in 1 year at $1,400

After 1 year you gross $70 (note that we have ignored the borrowing cost of the short position in the gold)

20

1. Oil: An Arbitrage Opportunity?

Suppose that:

- The spot price of oil is US$95 - The quoted 1-year futures price of

oil is US$125

- The 1-year US$ interest rate is 5% per annum

- The storage costs of oil are 2% per annum

Is there an arbitrage opportunity?

21

The Forward Price of Oil

If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then

F = S (1+r )T

where r is the 1-year (domestic currency) risk-free rate of interest.

In our examples, S = 95, T = 1, and r =0.05 so that

F = 95(1+0.05) = $99.75

22

1. Oil: An Arbitrage Opportunity?

23

Borrow $95 at 5%, use to buy oil, then pay back loan in 1 year time $99.75

Storage cost 2% of $95 = $1.9

Sell 1 year futures $125

Total cost $99.75 + $1.9 = $101.65

Receive $125

Profit = $23.35

Options A call option is an option to buy a certain asset by a

certain date for a certain price (the strike price)

A put option is an option to sell a certain asset by a

certain date for a certain price (the strike price)

Traded both OTC and on exchange

24

American vs European Options

An American option can be exercised at any time during its life

A European option can be exercised only at maturity

Most exchange traded are American options

Exchange traded equity options are usually an agreement to buy or sell 100 shares.

OTC options can have virtually any condition, which are agreed on by both counterparties

25

Google Call Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25) Source: CBOE

26

Strike

Price

Jul 17

2010 Bid

Jul 17

2010

Offer

Sep 18

2010 Bid

Sep 18

2010 Offer

Dec 18

2010 Bid

Dec 18

2010

Offer

460 43.30 44.00 51.90 53.90 63.40 64.80

480 28.60 29.00 39.70 40.40 50.80 52.30

500 17.00 17.40 28.30 29.30 40.60 41.30

520 9.00 9.30 19.10 19.90 31.40 32.00

540 4.20 4.40 12.70 13.00 23.10 24.00

560 1.75 2.10 7.40 8.40 16.80 17.70

Google Put Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25); Source: CBOE

27

Strike

Price

Jul 17

2010 Bid

Jul 17

2010

Offer

Sep 18

2010 Bid

Sep 18

2010 Offer

Dec 18

2010 Bid

Dec 18

2010

Offer

460 6.30 6.60 15.70 16.20 26.00 27.30

480 11.30 11.70 22.20 22.70 33.30 35.00

500 19.50 20.00 30.90 32.60 42.20 43.00

520 31.60 33.90 41.80 43.60 52.80 54.50

540 46.30 47.20 54.90 56.10 64.90 66.20

560 64.30 66.70 70.00 71.30 78.60 80.00

Class exercise

28

You want to buy one December call option on Google with strike of $520

Offer price is $32.00, this is for an option to buy one share, but exchange traded are on 100 shares

So you need $3,200 to buy contract

You now have the right to buy 100 Google shares at $520 each on December 18th 2010.

Consider 3 market scenarios after 6 months.

i) Google < $520 ii) Google =$530 iii) Google = $600

Alternative strategy

Sell one September put option with strike price of $480

Price is $22.20 for 1 (remember you have to agree on 100 shares)

Cash inflow = $2,220 (Youve sold the put contract)

If Google share price remains above $480 by 18th September, you will earn $2,220, because the trader will not exercise the put option

If shares = $420 at maturity

You must buy 100 shares at $480 = $48,000, but they are only worth $420

= $3,780 total loss when accounting for the cash inflow from selling of put

29

Options vs Futures/Forwards

A futures/forward contract gives the holder

the obligation to buy or sell at a certain

price

An option gives the holder the right to buy

or sell at a certain price but not the

obligation

30

Forward/futures payoffs

31

Option payoffs

32

What can derivatives be used for

Hedging

Speculating

Arbitrage

33

Hedge example using forward

A US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract

34

Foreign Exchange Quotes for GBP, May 24, 2010

35

Bid Offer

Spot 1.4407 1.4411

1-month forward 1.4408 1.4413

3-month forward 1.4410 1.4415

6-month forward 1.4416 1.4422

Exporter can hedge against FX risks with a 3-month forward contract

3-month offer quote is 1.4415, in effect this fixes the prices to be paid to $14,415,000 = 10,000,000

The hedge can work in favour of the company or not.

Scenario 1: Ex rate is 1.3 on 24 Aug, company will wish it had not hedged because,

10,000,000 is only worth $13,000,000, but company is locked in at $14,415,000!

Scenario 2: Ex rate is 1.5, company is glad it has hedged otherwise it would have cost them $15,000,000 to deliver the 10m

Risk vs reward

36

Hedge example using forward

Hedge example using options

An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts

This investor is concerned about Microsoft share loosing value

Remember exchange traded options must be bought by the 100s..

10 contracts = put option on 1,000 shares

Total cost of hedge is $1,000

37

Hedge example using options

Hedge costs $1,000 but guarantees sale of shares for $27.50

If share price falls below $27.50, the investor will exercise option, and sell shares for $27,500.

Taking into account option cost = $26,500 for investor

If share price stays above $27.50, option will not be exercised, but investor will still get back more than $26,500

If at $28.00, investor will get $27,000 (taking option cost into account.

Due to cost of the hedge, investor will always be $1,000 worse off if share price is above $27.50

38

Value of Microsoft Shares with and without Hedging

39

20,000

25,000

30,000

35,000

40,000

20 25 30 35 40

Value of Holding ($)

Stock Price ($)

No Hedging

Hedging

Forwards/futures vs options

Forwards/futures neutralise risk by fixing the price paid or received for underlying asset

Option contracts provide insurance, because there is limited downfall, whilst allowing benefit from favourable price movements

Downside of option is the cost/premium

Forwards/futures have no upfront cost/premium

40

Speculation Class exercise

An investor with $2,000 to invest feels that

a stock price will increase over the next 2

months. The current stock price is $20 and

the price of a 2-month call option with a

strike of 22.50 is $1

What are the strategies?

Consider

i) Buying shares ii) Buying call options

41

Margins

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

Margins minimize the possibility of a loss through a

default on a contract

Forwards are different, there are risks, counterparty may

not have financial resources to honor contract

Forwards are settled at maturity, whilst Futures are

settled daily

Futures are rarely held till maturity

42

Review of Option Types

A call is an option to buy

A put is an option to sell

A European option can be exercised only

at the end of its life

An American option can be exercised at

any time

43

Option Positions

Long call

Long put

Short call

Short put

44

Long Call Profit from buying one European call option: option

price = $5, strike price = $100, option life = 2 months

45

30

20

10

0 -5

70 80 90 100

110 120 130

Profit ($)

Terminal

stock price ($)

Short Call Profit from writing one European call option: option

price = $5, strike price = $100

46

-30

-20

-10

0 5

70 80 90 100

110 120 130

Profit ($)

Terminal

stock price ($)

Long Put Profit from buying a European put option: option

price = $7, strike price = $70

47

30

20

10

0

-7 70 60 50 40 80 90 100

Profit ($)

Terminal

stock price ($)

Short Put Profit from writing a European put option: option

price = $7, strike price = $70

48

-30

-20

-10

7

0 70

60 50 40

80 90 100

Profit ($) Terminal

stock price ($)

Payoffs from Options What is the Option Position in Each Case?

K = Strike price, ST = Price of asset at maturity

49

Payoff Payoff

ST ST K

K

Payoff Payoff

ST ST K

K

Payoff = max(ST K, 0) Payoff = -max(ST K,

0)

Payoff = -max(K - ST, 0)

Payoff = max(K - ST, 0)

Assets Underlying Exchange-Traded Options

Stocks

Foreign Currency

Stock Indices

Futures

50

Specification of Exchange-Traded Options

Expiration date

Strike price

European or American

Call or Put (option class)

51

Terminology

Moneyness : At-the-money option

In-the-money option

Out-of-the-money option

52

Calls:

ATM Strike = Spot

ITM Strike < Spot

OTM Strike > Spot

Puts:

ATM Strike = Spot

ITM Strike > Spot

OTM Strike < Spot

Google Call Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25) Source: CBOE

53

Strike

Price

Jul 17

2010 Bid

Jul 17

2010

Offer

Sep 18

2010 Bid

Sep 18

2010 Offer

Dec 18

2010 Bid

Dec 18

2010

Offer

460 43.30 44.00 51.90 53.90 63.40 64.80

480 28.60 29.00 39.70 40.40 50.80 52.30

500 17.00 17.40 28.30 29.30 40.60 41.30

520 9.00 9.30 19.10 19.90 31.40 32.00

540 4.20 4.40 12.70 13.00 23.10 24.00

560 1.75 2.10 7.40 8.40 16.80 17.70

Google Put Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25); See Table 1.3 page 9; Source: CBOE

54

Strike

Price

Jul 17

2010 Bid

Jul 17

2010

Offer

Sep 18

2010 Bid

Sep 18

2010 Offer

Dec 18

2010 Bid

Dec 18

2010

Offer

460 6.30 6.60 15.70 16.20 26.00 27.30

480 11.30 11.70 22.20 22.70 33.30 35.00

500 19.50 20.00 30.90 32.60 42.20 43.00

520 31.60 33.90 41.80 43.60 52.80 54.50

540 46.30 47.20 54.90 56.10 64.90 66.20

560 64.30 66.70 70.00 71.30 78.60 80.00