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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.

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## Engines of the Economy or Instruments of Mass Destruction?

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**Engines of the Economy orInstruments 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 SELLan 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) = 120So 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) = 117So, 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 coffeeOptions allow the redistribution of risk!Derivatives = giant insurance enterprise ?**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 : Engineering of derivatives:**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.

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