IIPM Derivative Overview

Financial Engineering and Derivatives Usage: An Overview

Suman Banerjee

IIPM, New DelhiJuly 12-13, 2008

The Nature of Derivatives

●A derivative is an instrument whose value depends on the values of other fundamentals (or more basic) underlying variables:○Stocks○Currencies○Commodities

Types of Derivatives

● Three common types of derivatives ○ Options

■ Future rights○ Swaps

■ Obligated Exchange of future cash flows

○ Futures (or Forward) Contracts■ Obligated future price or rate

PAYMENTPresent

Future Forward(Future)

Borrowing

Lending

Present

Future

RECEIPT

Cash

Asset Identification Matrix

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

S&P 500 Futures and Options ContractsTuesday, September 5, 2004

Closing S&P 500 Index: 1113.60

––– Delivery/Expiration Month ––– Type Strike Nov Dec Jan Mar JunFuture 1117.60 1117.20 1129.00Call 1113 15.10 22.30 30.70 Call 1123 8.35 15.95 24.05Call 1133 3.60 10.65 18.10Put 1113 3.85 11.15 13.35Put 1123 7.10 14.70 16.60Put 1133 12.35 19.35 20.50

Sample Derivatives Prices

Ways Derivatives Are Used

●To hedge risks●To lock in an arbitrage profit●To change the nature of an

investment without incurring the costs of selling one portfolio and buying another

Common Terminology

●The party that has agreed to:○BUY has what is termed a

LONG position

○SELL has what is termed a SHORT position

Continuous Compounding

● We will calculate the present and future values of cash flows assuming continuous compounding

where r = interest rate t = holding periode = exponential coefficient=2.7183

Example

● January: an investor enters into a long futures contract on COMEX to buy 100 oz of gold @ $300/oz in April 2005

● April: the price of gold $315 per oz ● What is the investor’s profit? $15/oz

January July

I’ll buy yourhouse in Julyfor $350,000.

You’ve gota deal.

Nothing is exchanged now.

Forwards

Thanks for the house.

Thanks forthe $350,000.

Trade occurs in the future.

Exchanges Trading Futures

●Chicago Board of Trade●Chicago Mercantile Exchange●BM&F (Sao Paulo, Brazil)●LIFFE (London)●TIFFE (Tokyo)

Gold: Arbitrage Opportunity?

● Suppose that:○ The spot price of gold is US$290○ The quoted 1-year futures price

of gold is US$315○ The 1-year US$ interest rate is

5% per annum● Is there an arbitrage opportunity?

Gold: Another Opportunity?

● Suppose that:○ The spot price of gold is US$290○ The today’s quoted 1-year futures

price of gold is US$315○ The 1-year US$ interest rate is

10% per annum● Is there an arbitrage opportunity?

Options

● A CALL is an option to BUY a certain asset by a certain date for a certain pre-specified price

● A PUT is an option to SELL a certain asset by a certain date for a certain pre-specified price

If you pay me$50,000 extranow, it’s a deal.

I’ll buy your house in July for $350,000,if I want to then.

CALLS: Price now; if buyer wants, he buys asset later.

January

� Housing Prices Fall

I’ve decidednot to buy.

That’s OK. ButI get to keepthe $50,000.

July

Thanks forthe house.


� Housing Prices Rise

Options: Long Call

● Profit from buying an European call option: option price = $50, strike price = $350, option life = 6 months

30

20

10

0-50

270

280

290

350

410

420

430

Profit ($)

Terminalstock price ($)

Options: Short Call

● Profit from writing European call option: option price = $50, strike price = $350, option life = 6 months

-30

-20

-10

050

270

280

290

350

410

420

430

Profit ($)

Terminalstock price ($)

If you pay me$50,000 extranow, it’s a deal.

I’ll sell you my house in July for $350, 000if I want to then.

PUTS: Price now; if option buyer wants, she sells asset later.


� Housing Prices Fall Thanks for

the house.

I’ve decidednot to sell.

That’s OK. ButI get to keepthe $50,000.

� Housing Prices Rise

Options: Long Put● Profit from buying an Tata European put option: option

price = INR 7, strike price = INR 70, option life = 3 months

70

50

30

0

-5070605040 80 90 100

Profit (INR)

Terminalstock price (INR)

Options: Short Put

● Profit from writing an Tata European put option: option price = INR 50, strike price = INR 350, option life = 6 months

-30

-20

-10

50

070

605040

80 90 100

Profit (INR)Terminal

stock price (INR)

Options: Zero-sum Game

Long Call Payoff Short Call Payoff

ST

ST

XX

Long Put Payoff Short Put Payoff

ST

ST

XX

I’m glad I bought thecall because now I can buy a $410,000 housefor only $350,000.

Too bad I sold that call; I had to sell myhouse cheaply.

� Housing Prices Riseto $410,000

$410,000- 350,000- 50,000$ 10,000

$- 410,000350,00050,000$ - 10,000

Options:“zero-sum Game”

$ - 50,000

$ 50,000

� Housing Prices Fall

Too bad I boughtthat call; it didn’tpay to exercise it.

I’m glad I sold thecall; I got paid forit and still keptmy house.

Exchanges Trading Options

●Chicago Board Options Exchange (CBOE)

●American Stock Exchange (AMEX)

●Philadelphia Stock Exchange●Pacific Stock Exchange●European Options Exchange●Australian Options Market

Futures Vs. Options

● A FUTURES contract gives the holder the OBLIGATION to buy or sell at a certain price

● Even if the price is unfavorable to the holder of the contract, the contracted trade is executed

● An OPTION gives the holder the RIGHT to buy or sell at a certain price

● If the prices are unfavorable to the holder of the contract, he can forgo the contracted trade

Motivations

Why use Options instead of Futures?● Preference for non-symmetric payoffs● Take advantage of information about the

shape of the subjective probability distribution of the underlying asset price

Types of Traders

●Hedgers●Speculators●Arbitrageurs

● Some of the large trading losses inderivatives occurred because individualswho had a mandate to hedge risksswitched to being speculators.

Hedging Using Options

●An investor owns 500 IBM shares currently worth $102 per share.

●A put with a strike price of $100 costs $4.

●The investor decides to hedge by buying 5 contracts.

○ Each contract implies right to sell 100 shares.

○ 5 contracts costs $2000.

Speculation Using Options

● An investor with $7,800 to invest feels that Exxon’s stock price will increase over the next 3 months.

● The current stock price is $78 and the price of 3-month call options with a strike of 80 is $3.

● What are the alternative strategies?

Dividends & Stock Splits

● Suppose you own N options with a strike price of X :○ No adjustments are made to the option

terms for cash dividends○ When there is an n-for-m stock split,

■ the strike price is reduced to mX/n ■ the no. of options is increased to nN/m

○ Stock dividends are handled in a manner similar to stock splits

Dividends & Stock Splits

● Consider a call option to buy 100 shares for $20/share

● How should terms be adjusted:○ for a 2-for-1 stock split?○ for a 20% stock dividend?

■ Equivalent to 6-for-5 stock split

Margins

● Margins are required when options are sold● When a naked option is written the margin is

the greater of:1. A total of 100% of the proceeds of the

sale plus 20% of the underlying share price less the amount (if any) by which the option is out of the money

2. A total of 100% of the proceeds of the sale plus 10% of the underlying share price

Margins● Suppose you are selling 4 naked call option

contracts with a strike price of $37 for $4 when the stock price is $35○ The first condition gives

400(4+0.2*35-2) = $3,600○ The first condition gives

400(4+0.1*35) = $3,000● Thus, the margin requirement is $3,600● What if the option was a PUT?

Swaps Contracts: Definitions

● In a swap, two counter-parties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals.

● There are two types of interest rate swaps:○ Single currency interest rate swap

■ “Plain vanilla” fixed-for-floating swaps are often just called interest rate swaps.

○ Cross-Currency interest rate swap■ This is often called a currency swap; fixed for fixed rate debt

service in two (or more) currencies.

The Swap Bank

● A swap bank is a generic term to describe a financial institution that facilitates swaps between counter-parties.

● The swap bank can serve as either a broker or a dealer.

○ As a broker, the swap bank matches counter-parties but does not assume any of the risks of the swap.

○ As a dealer, the swap bank stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counter-party.

An Example of an Interest Rate Swap

● Consider this example of a “plain vanilla” interest rate swap.

● Bank A is a AAA-rated international bank located in the U.K. and wishes to raise $10,000,000 to finance floating-rate Eurodollar loans.

○ Bank A is considering issuing 5-year fixed-rate Eurodollar bonds at 10%.

○ It would make more sense to for the bank to issue floating-rate notes at LIBOR to finance floating-rate Eurodollar loans.


● Firm B is a BBB-rated U.S. company. It needs $10,000,000 to finance an investment with a five-year economic life.

○ Firm B is considering issuing 5-year fixed-rate Eurodollar bonds at 11.75%.

○ Alternatively, firm B can raise the money by issuing 5-year floating-rate notes at LIBOR + ½ percent.

○ Firm B would prefer to borrow at a fixed rate.


The borrowing opportunities of the two firms are:


Bank

A

The swap bank makes this offer to Bank A: You pay LIBOR – 1/8 % per year on $10 million for 5 years and we will pay you 10 3/8% on $10 million for 5 years

Swap

Bank

LIBOR – 1/8%

10 3/8%

An Example: Interest Rate SwapHere’s what’s in it for Bank A: They can borrow externally at 10% fixed and have a net borrowing position of

-10 3/8 + (LIBOR – 1/8) +10 = LIBOR – ½ %

which is ½ % better than they can borrow floating without a swap.

10%

½% of $10,000,000 = $50,000. That’s quite a cost savings per year for 5 years.

Swap

Bank

LIBOR – 1/8%

10 3/8%

Bank A


Company B

The swap bank makes this offer to company B: You pay us 10½% per year on $10 million for 5 years and we will pay you LIBOR – ¼ % per year on $10 million for 5 years.

Swap

Bank10 ½%

LIBOR – ¼%


They can borrow externally at

LIBOR + ½ % and have a net

borrowing position of

10½ + (LIBOR + ½ ) - (LIBOR - ¼ ) = 11.25% which is ½% better than they can borrow fixed.

LIBOR + ½%

Here’s what’s in it for B:½ % of $10,000,000 = $50,000 that’s quite a cost savings per year

for 5 years.Swap Bank

Company B

10 ½%LIBOR – ¼%


The swap bank makes money too. ¼% of $10 million = $25,000 per

year for 5 years.

LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8

10 ½ - 10 3/8 = 1/8

¼

Swap Bank

Company B

10 ½%LIBOR – ¼%LIBOR – 1/8%

10 3/8%

Bank A


Swap Bank

Company

B

10 ½%LIBOR – ¼%LIBOR – 1/8%

10 3/8%

Bank

AB saves ½%A saves

½%

The swap bank makes ¼%

Documents

IIPM Derivative Overview