Engines of the Economy or

Instruments of Mass Destruction?

The magic of

Financial DerivativesKlaus VolpertVillanova UniversityMarch 22, 2000

I can think of no other area that has the potential of creating greater havoc on a

global basis if something goes wrongDr. Henry Kaufman, May 1992

Derivatives are the dynamite for Derivatives are the dynamite for financial crises and the fuse-wire financial crises and the fuse-wire for international transmission at for international transmission at the same timethe same time.. Alfred Steinherr, author of Derivatives: The Wild Beast of Finance (1998)

What is a Financial Derivative?

• A security created by contract which derives its value from an underlying asset, such as shares or bonds.

• For example:– stock options– oil futures– interest rate swaps

Two Basic Kinds of Options

• A (European) Call Option is the right to BUY an underlying asset – at prescribed future time T (time of expiry)– for a prescribed price X (strike price)

• A Put Option is the right to SELL an underlying asset at time T for a price X.

• The buyer of an option is known as the Holder, the seller is the Writer

Example: A Call on IBM

• Option to buy an IBM share at $120 6 months from now. Currently the price of an IBM share is $100.

Question: What would you pay for this option??

Example: A Put on IBM

• Option to SELL an IBM share at $120 6 months from now. Currently the price of an IBM share is $100.

What would you pay for this?

Price can be determined by

• The market (like an auction)

• mathematical analysis:in 1973, Black and Scholes came up with a model to price options.

It was an instant hit, and became the sine-qua-non of the options market until 1987.

A first example of mathematical analysis: the Put-Call Parity

• The prices of a put and a call on the same asset with the same parameters are linked:

Suppose we buy a share of IBM at $100. We also buy a put of value P and sell a call at price C with the same strike X=120 and the time of expiry T. How much money will we spend on this portfolio?

Answer: 100 + P - C

At time of expiry what is our payoff?Answer: if S is the IBM share price at time T, and

If S>120, payoff = S - (S - 120) = 120 If S<120, payoff = S +(120 - S) = 120

So this portfolio is risk-free! Its fair market price should be the same as for the benchmark treasury bond - which is

$120 discounted to the present time. So

100 + P - C = 120 exp(-r*T) = 117

So, P - C = 17

The Black-Scholes Formula• Devised a riskless portfolio consisting just of

the option to be evaluated and a fluctuating number of shares

• assumed a randomwalk of share prices

• plugged that into Ito’s Formula, to get

• a partial differential equation that determines the price of the option

±V±t+1=2¾2S2±2V±S2+rS±V±S¡rV=0

±V±t+1=2¾2S2±2V±S2+rS±V±S¡rV=0

±V±t+1=2¾2S2±2V±S2+rS±V±S¡rV=0

±V±t+1=2¾2S2±2V±S2+rS±V±S¡rV=0

±V±t+1=2¾2S2±2V±S2+rS±V±S¡rV=0

22 2

2

10

2

V V VS rS rV

t S S

Who would invest in options and why?

• You profit from holding call options if the market is going up.

• You profit from holding put options if prices are going down.

Who would invest in options and why?

• Hedging a risk:– if you own IBM and you are worried about a down

turn, you buy put options as insurance.

– If you are a Starbucks franchise owner + worried about the price of coffee - you buy call options on coffee

Options allow the redistribution of risk!Derivatives = giant insurance enterprise ?

Engineering of derivatives:• Buy a call with strike 120,

buy a put with strike 80 (a strangle). Then a payoff-

minus-cost diagram would look like

• In addition sell a call and a put with strike 100 (known as a butterfly). payoff-minus-cost diagram :

Who would invest in options and why?

• Speculation: the movement of stocks is greatly amplified by options:

Consider the option to buy IBM at $120 in half a year:– if the current price is $100, then the price of the option

(according to Black-Scholes) is $1,– if the share price jumps tomorrow to $110, the price of

the option jumps to $3.50

So, while the underlying stock price has gone up 10 %, the value of the option has gone up 250%!

This is called leveraging.

By buying options instead of assets, you can magnify your risk / your potential payoff

almost without limit.

Cause for Concern?

• 1987 crash: investors who sold ‘naked puts’ lost everything and then some.

• 1994: Orange County: losses of $1.7 billion

• 1995: Barings Bank: losses of $1.5 billion

• 1996: Sumitomo bank: losses of $2.6 billion

• 1998: LongTermCapitalManagement (LTCM) hedge fund, founded by Meriwether, Merton and Scholes. Losses of over $2 billion

1997: Merton and Scholes win Nobel prize in Economics

• Cheers in The Economist: The professors have turned risk management from a guessing game into a science

• Jeers in Barron’s: The pair snared the rich honor, and the tidy sum that goes with it, for devising a formula to measure the worth of a stock option, thus paving the way for both the spectacular growth of options and their use as instruments of mass destruction.