The theory that promised so much

November 19, 1999

The key to Black, Scholes and Merton's work - that derivatives can be replicated - is best illustrated by an example. Suppose you own a share worth Pounds 100 today. But in one month it will either rise to Pounds 110 or drop to Pounds 90.

Suppose also that you have sold a pair of options to a friend, each giving her the right to buy one such share at Pounds 100 one month from now. What can happen in a month?

If your share value rises, your friend can come to you and buy two shares for Pounds 100 each. To honour the contract you must buy the shares in the market at a price of Pounds 110, then hand them over. The result is a pay-out of Pounds 20 and although the single share you own is worth Pounds 10 more, you have lost Pounds 10 on the deal.

If the share value falls, the option you have sold is worthless, but your share is worth only Pounds 90, so again you have lost Pounds 10. The price you charge your friend for a single option should be Pounds 5 -to break even.

By trading shares against the value of options they have sold, traders can immunise themselves against market movement. The price of an option must match the cost of replicating it in this way.

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