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… 1

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 2

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 3

Size of OTC and Exchange-Traded Markets (Figure 1.1, Page 3)

Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market 4

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 5

Foreign Exchange Quotes for GBP, May 24, 2010

Spot Bid 1.4407

Offer 1.4411

1-month forward 3-month forward 6-month forward 1.4408

1.4410

1.4416

1.4413

1.4415

1.4422

6

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) 7

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 8

Example

(page 5)

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?

9

Profit from a Long Forward Position

(K= delivery price=forward price at time contract is entered into)

Profit

K

Price of Underlying at Maturity,

S T

10

Profit from a Short Forward Position

(K= delivery price=forward price at time contract is entered into)

Profit

K

Price of Underlying at Maturity,

S T

11

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 12

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 13

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 14

1. Gold: An Arbitrage Opportunity?

Suppose that: The spot price of gold is US$1,400 The 1-year forward price of gold is US$1,500 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity? 15

2. Gold: Another Arbitrage Opportunity?

Suppose that: The spot price of gold is US$1,400 The 1-year forward price of gold is US$1,400 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?

16

The Forward Price of Gold

(ignores the gold lease rate)

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

= 1400,

T

= 1, and

r

so that =0.05

F

= 1400(1+0.05) = 1470 17

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) 18

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 19

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 20

Option Positions

Long call Long put Short call Short put 21

Long Call

Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months 30 Profit ($) 20 10 0 -5 70 80 90 100 Terminal stock price ($) 110 120 130 22

Short Call

Profit from writing one European call option: option price = $5, strike price = $100 Profit ($) 5 0 110 120 130 -10 70 80 90 100 Terminal stock price ($) -20 -30 23

Long Put

Profit from buying a European put option: option price = $7, strike price = $70 30 Profit ($) 20 10 0 -7 40 50 60 70 80 90 Terminal stock price ($) 100 24

Short Put

Profit from writing a European put option: option price = $7, strike price = $70 7 0 Profit ($) 40 50 60 70 -10 80 90 Terminal stock price ($) 100 -20 -30 25

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

K

= Strike price,

S T

= Price of asset at maturity Payoff Payoff

K

Payoff

K S T S T

Payoff

K K S T S T

26

Assets Underlying Exchange-Traded Options

Stocks Foreign Currency Stock Indices Futures 27

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 28

Types of Traders

Hedgers Speculators Arbitrageurs 29

Swaps

A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 30

An Example of a “Plain Vanilla” Interest Rate Swap

An agreement by Microsoft to receive 6 month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows that could occur (Day count conventions are not considered) 31

One Possible Outcome for Cash Flows to Microsoft (Table 7.1, page 150)

Date LIBOR Mar 5, 2012 Sep 5, 2012 Mar 5, 2013 Sep 5, 2013 Mar 5, 2014 Sep 5, 2014 Mar 5, 2015 4.20% 4.80% 5.30% 5.50% 5.60% 5.90% Floating Cash Flow Fixed Cash Flow +2.10

+2.40

+2.65

+2.75

+2.80

+2.95

−2.50

−2.50

−2.50

−2.50

−2.50

−2.50

Net Cash Flow −0.40

−0.10

+ 0.15

+0.25

+0.30

+0.45

32

Typical Uses of an Interest Rate Swap

Converting a liability from fixed rate to floating rate floating rate to fixed rate Converting an investment from fixed rate to floating rate floating rate to fixed rate 33