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B. Venkatesh

THOSE familiar with the Black and Scholes (B&S) model may know that it does not use stock returns as a factor to price options.

This is because the model is based on the principles of replication and no-arbitrage. What are these principles?

Suppose you hold a stock at Rs 100. Assume that it can move by 10 per cent to Rs 90 or Rs 110 in one month.

You sell one call option on the stock. If the stock moves to Rs 110, you will lose Rs 10. Why?

If the call buyer exercises the option, you will deliver the stock at Rs 100 even though it trades at Rs 110.

If the stock declines to Rs 90, the option will expire worthless.

But you still lose Rs 10 on the stock that you are holding. You will, therefore, sell the call option at Rs 10 to breakeven.

So, if you hold a stock and sell suitable number of call options, you are not exposed to the market risk.

This is the principle of replication.

It does, however, make a difference whether the stock moves by 10 per cent or 20 per cent.

Higher the volatility, higher the option premium you will demand because of higher risk.

In the above example, why should the option sell for Rs 10 and not for more or less?

Suppose the call option trades at Rs 15. You can buy the stock at Rs 100 and sell the option. If stock ends at Rs 110, the option will then be worth Rs 10.

So, you can buy back the option and pocket Rs 5 as profit. Since the market is smart, it will price the option at Rs 10.

This is the no-arbitrage principle.

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