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MGT 821/ECON 873

Financial Derivatives

Lecture 1Introduction

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What is a derivative?

A derivative is an instrument whose value depends on the values of other more basic underlying variables

Example:

Forward Contracts, futures contracts

Swaps

Options

Credit derivatives

Derivatives Markets

Exchange Traded standard products trading floor or computer trading virtually no credit risk

Over-the-Counter non-standard products telephone market some credit risk

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Ways 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

Forward Contracts

A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) It can be contrasted with a spot contract which is an agreement to

buy or sell immediately The contract is an over-the-counter (OTC) agreement

between 2 companies The delivery price is usually chosen so that the initial

value of the contract is zero No money changes hands when contract is first

negotiated and it is settled at maturity

The 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

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Profit from a Long Forward Position

Profit

Price of Underlying at Maturity, STK

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Profit from a Short Forward Position

Profit

Price of Underlying at Maturity, STK

Example

On August 20, 2006 a trader enters into an agreement to buy £1 million in three months at an exchange rate of 1.6196

This obligates the trader to pay $1,619,600 for £1 million on November 20, 2006

What are the possible outcomes?

Profit from aLong Forward Position

Profit

Price of Underlying

at Maturity, STK

Profit from a Short Forward Position

Profit

Price of Underlying

at Maturity, STK

Futures - similar to forward but feature formalized and standardized characteristics Agreement to buy or sell an asset for a certain price at a certain time

Whereas a forward contract is traded OTC a futures contract is traded on an exchange

Key difference in futures Exchange traded Specifications need to be defined:

What can be delivered, Where it can be delivered, When it can be delivered

Settled daily

Futures

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Options

A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)

Exotic options

A put is an option to sell a certain asset by a certain date for a certain price (the strike price)

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Long Call on IBM

Profit from buying an IBM European call option: option price = $5, strike price = $100, option life = 2 months

30

20

10

0-5

70 80 90 100

110 120 130

Profit ($)

Terminalstock price ($)

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Short Call on IBM

Profit from writing an IBM European call option: option price = $5, strike price = $100, option life = 2 months

-30

-20

-10

05

70 80 90 100

110 120 130

Profit ($)

Terminalstock price ($)

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Long Put on Exxon

Profit from buying an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths

30

20

10

0

-770605040 80 90 100

Profit ($)

Terminalstock price ($)

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Short Put on Exxon Profit from writing an Exxon European put option: option price =

$7, strike price = $70, option life = 3 mths

-30

-20

-10

7

070

605040

80 90 100

Profit ($)Terminal

stock price ($)

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Payoffs from Options

Payoff Payoff

ST STK

K

Payoff Payoff

ST STK

K

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Swaps

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

Basic forms of swaps Interest rate swaps; currency swaps

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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

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Cash Flows to Microsoft

---------Millions of Dollars---------

LIBOR FLOATING FIXED Net

Date Rate Cash Flow Cash Flow Cash Flow

Mar.5, 2001 4.2%

Sept. 5, 2001 4.8% +2.10 –2.50 –0.40

Mar.5, 2002 5.3% +2.40 –2.50 –0.10

Sept. 5, 2002 5.5% +2.65 –2.50 +0.15

Mar.5, 2003 5.6% +2.75 –2.50 +0.25

Sept. 5, 2003 5.9% +2.80 –2.50 +0.30

Mar.5, 2004 6.4% +2.95 –2.50 +0.45

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Typical Uses of anInterest 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

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Currency Swap

Example

An agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US$ principal of $15,000,000 every year for 5 years

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The Cash Flows

Year$

------millions------

2001 –15.00 +10.002002 +1.20 –1.10

2003 +1.20 –1.10 2004 +1.20 –1.10

2005 +1.20 –1.10 2006 +16.20 -11.10

£

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Typical Uses of a Currency Swap Conversion from a

liability in one currency to a liability in another currency

Conversion from an investment in one currency to an investment in another currency

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Credit Risk

A swap is worth zero to a company initially At a future time its value is liable to be either

positive or negative The company has credit risk exposure only

when its value is positive

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Swaptions

What is a swaption Swap rate

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Credit Derivatives

Credit Default Swap Company A buys default protection from B to

protect against default on a reference bond issued by the reference entity, C.

A makes periodic payments to B In the event of a default by C

A has the right to sell the reference bond to B for its face value, or

B pays A the difference between the market value and the face value

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CDS Structure

Default Protection Buyer, A

Default Protection Seller, B

90 bps per year

Payment if default by reference entity,C

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Other credit derivatives

First-to-default Total return swap Credit spread option CDO