Greeks

The options premium is determined by the three factors mentioned earlier – intrinsic value, time value and volatility. But there are more sophisticated tools used to measure the potential variations of options premiums. They are as follows:

• Delta
• Gamma
• Vega
• Rho

Delta

Delta is the measure of an option's sensitivity to changes in the price of the underlying asset. Therefore, its is the degree to which an option price will move given a change in the underlying stock or index price, all else being equal.

Change in option premium
Delta = --------------------------------
Change in underlying price

For example, an option with a delta of 0.5 will move Rs 5 for every change of Rs 10 in the underlying stock or index.

Illustration:

A trader is considering buying a Call option on a futures contract, which has a price of Rs 19. The premium for the Call option with a strike price of Rs 19 is 0.80. The delta for this option is +0.5. This means that if the price of the underlying futures contract rises to Rs 20 – a rise of Re 1 – then the premium will increase by 0.5 x 1.00 = 0.50. The new option premium will be 0.80 + 0.50 = Rs 1.30.

Far out-of-the-money calls will have a delta very close to zero, as the change in underlying price is not likely to make them valuable or cheap. An at-the-money call would have a delta of 0.5 and a deeply in-the-money call would have a delta close to 1.

While Call deltas are positive, Put deltas are negative, reflecting the fact that the put option price and the underlying stock price are inversely related. This is because if you buy a put your view is bearish and expect the stock price to go down. However, if the stock price moves up it is contrary to your view therefore, the value of the option decreases. The put delta equals the call delta minus 1.

It may be noted that if delta of your position is positive, you desire the underlying asset to rise in price. On the contrary, if delta is negative, you want the underlying asset's price to fall.

Uses:

The knowledge of delta is of vital importance for option traders because this parameter is heavily used in margining and risk management strategies. The delta is often called the hedge ratio. e.g. if you have a portfolio of 'n' shares of a stock then 'n' divided by the delta gives you the number of calls you would need to be short (i.e. need to write) to create a riskless hedge – i.e. a portfolio which would be worth the same whether the stock price rose by a very small amount or fell by a very small amount.

In such a "delta neutral" portfolio any gain in the value of the shares held due to a rise in the share price would be exactly offset by a loss on the value of the calls written, and vice versa.

Note that as the delta changes with the stock price and time to expiration the number of shares would need to be continually adjusted to maintain the hedge. How quickly the delta changes with the stock price is given by gamma, which we shall learn subsequently.

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