# Web Exclusive Here's how traders can use delta and gamma for options trading

Option Greeks are basically about sensitivities. We are familiar with the Black and Scholes formula to calculate the value of the option. But then a trader is more worried about sensitivities. These Option Greeks measure how the option value is vulnerable to changes in various variables like the market price, interest rates, volatility, time to expiry etc. Two very important and closely related Greeks are Delta and Gamma. Let us look at them in greater detail.

Understanding Option Delta

Option delta measures the sensitivity of the price of an option (intrinsic value) to the changes in the market price of the underlying. For example, if we are looking at a Reliance 1,250 call option expiring on the last Thursday of March 2019 then delta will measure how the option price of this particular contract moves with respect to changes in the price of Reliance spot. An option delta of a call option will vary from 0 to 1 while the option delta of a put option will vary from 0 to -1. Generally, the delta is the highest for an in-the-money call option and it will be close to 1 while it will be closer to 0 in case of out-of-the-money call option. Effectively, call options will have a positive delta while put options will have a negative delta.

Different traders use different scales for measuring option delta. While some use a scale of 0 to 1, others use a scale of 0-100. So a delta value of 0.60 will be equivalent to 60 in the other scale, but the underlying concept remains the same. What does a delta of 0.60 really mean? It shows the sensitivity of the price of the option to shifts in the price of the underlying. If the RIL stock moves up by Rs.20 then the price of the call option with a delta of 0.6 will move up by Rs 12. Similarly, the price of a put option with Delta of -0.60 will move lower by Rs 12 since put options are negatively related to the stock price.

• Delta can also be seen as the probability of the option expiring in the money (ITM). Which is why an ATM option has delta of around 0.5 (50-50 chance), deep ITM options have delta closer to 1 and deep OTM options have delta closer to 0.
• Delta is positive for call options and negative for put options. That is because a rise in price of the stock is positive for call options but negative for put options. A positive delta means that you are long on the market and a negative delta means that you are short on the market.
• Delta keeps changing over a period of time. Delta depends on factors like volatility, interest rates and time to maturity
How traders can use delta for hedging their risk?

Delta hedging reduces the risk of price movements in the underlying asset by offsetting long and short positions. If the trader holds one call option with a delta of 0.50 and one put option with a delta of -0.50 then the net delta of the position is 0. Typically, straddles have a zero delta. Delta hedging can also be done with stocks and options. How does it work? Let us say you are holding a call option with a delta of 0.70. If the lot size of the stock is 1000 shares then you can perfectly hedge 1 lot of the call option by selling 700 shares of the stock.

Getting down to Gamma, the second level of delta

If option delta measures the sensitivity of the option price to changes in the price of the underlying asset, Gamma is the second level measure of the sensitivity of changes in delta to changes in the underlying stock price. Gamma answers the question, “how much does the delta change in response to stimuli like interest rates, volatility and time to expiry”? Effectively, Delta is a measure of the rate of change in the option premium whereas gamma measures the momentum. In other words, gamma measures movement risk.

Like delta, the gamma value will also ranges between 0 and 1. Gammas are linked to whether your option is long or short in the market. So if you are long on a call option or long on a put option then your gamma will be positive. But, if you are short on a call option or short on a put option then your gamma will be negative.

How traders can apply gamma in practice?

The gamma is the highest when the strike price is very close to the stock price i.e. in case of ATM options. That is the time when the impact on the delta is the maximum. As the options become very deep ITM or deep OTM, the impact on delta is minimal. Therefore, the gamma curve will reflect that. It will be more of a bell shaped curve and as you go deep OTM or deep ITM, the bell curve starts becoming flat.

Assume a stock is quoting at Rs.850 and there is an OTM 870 call option that is quoting at Rs.18. This stock has delta of 0.4(40%) and a gamma of 0.1(10%). What happens to Delta and Gamma when the stock price moves up from Rs.850 to Rs.880?

• Since the delta is 0.4, the call option price will move up by 0.4 x (30) {Delta times change in the price of the underlying}. Thus the 870 call option price will move up by Rs.12 from Rs.18 to Rs.30.
• What happens to the delta? The delta will move up by the extent of the gamma in the above case. That is because the gamma measures the sensitivity of the delta to shifts in the stock price.
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Disclaimer: The above opinion is that of Mr. Sneha Seth (Derivatives Analyst- Angel Broking) & is for reference only.