Engines of the Economy or Instruments of Mass Destruction? The magic of Financial Derivatives Klaus Volpert Villanova University March 22, 2000

I can think of no other area that has the potential of creating greater havoc on a global basis if something goes wrong Dr. Henry Kaufman, May 1992 Derivatives are the dynamite for financial crises and the fuse-wire for international transmission at the 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: 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 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

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.