Buying and selling options are slightly more complicated that buying and selling futures. That is because futures are linear products while options are non-linear products. Whether you are long or short on a future, your profit profile is quite clear. If you are long and the price goes up then there is a profit and if the price goes down there is a loss.Options became non-linear for the buyer and the seller. For the buyer, the profits are unlimited but the losses are limited to the extent of the premium paid. For the seller, the losses can be unlimited but the profits are limited to the extent of the premium received. It is this non-linearity of returns of options that makes more complex and vulnerable to a host of other factors.

One of the techniques of evaluating options is the concept of Option Greeks. There are a variety of Greeks like Theta,Delta, Gamma, Rho and Vega. Each of these Greeks measures the sensibility of the option price to changes in external factor. One of the most important Greeks with respect to options is Delta, which measures the sensitivity of the option premium to changes in price of the underlying asset. If we are referring to the Nifty September 2017 option then the Delta will measure the sensitivity of the option premium to shifts in the spot price of the Nifty.

**The long and short of ****deltas..**

Both the call options and the put options have delt as because both calls and puts tend to get impacted by price movements in the underlying. For example, if the spot price of the Nifty index goes up then the price of the call option will go up and if the spot Nifty goes down then the price of the put option will go up. Since a call option has a positive relationship with the underlying price it always has a positive delta while the put option will always have a negative delta because of its inverse relationship with the spot price of the Nifty.

In case of call options, the delta will typically range from 0 to 1 and in case of put options the delta will range from 0 to -1.That is why call options are said to have positive delta while put options are said to have negative delta.

**Nature of Position**

**Nature of profits**

**Nature of movement**

**Nature of Delta**

Long on Call Option

Unlimited

Positive with Index

Positive Delta

Long on Put Option

Unlimited

Negative with Index

Negative Delta

Short on Call Option

Limited to Premium

Negative with Index

Negative Delta

Short on Put Option

Limited to Premium

Positive with Index

Positive Delta

**Applying Delta for Delta hedging..**

It is one thing to understand the concept of delta but what is more important is to understand the practical application of Delta. How do options traders use the concept of delta to take practical decisions? It needs to be understood that an At-The-Money (ATM) option will always have a delta of around 0.50. Therefore an Out-of-the-money (OTM) option will have a delta lower than 0.50.

Let us understand this with an example of how Delta can be used for hedging your risk more scientifically and precisely.Assume that a trade is expecting the Nifty to go up and has bought 5 lots of Nifty 10,000 Call Options at a premium or Rs.55. Since the spot Nifty is currently quoting at Rs.9920, the above call option will be an OTM call option.Hence the entire premium will be in the nature of time value only. As we have seen earlier, an OTM option will typically have a delta of less than 0.50. For the sake of simplicity let us assume that the delta of this particular call options is 0.40.

A day after the trade was initiated, the US Fed announced a hike in rates and the trader was sceptical that if the markets move down further he may lose the entire premium on his options. He therefore decided to delta hedge his options potions position. He can hedge his position by selling delta equivalent number of futures lots. Now Futures will always have a delta of 1 as the futures tends to move in proportion to the spot price.So, the 5 lots of call options can be hedged by selling 2 lots (5 lots of options X Delta of 0.4) of Nifty Futures. The table below captures how the delta hedged position will look like..

**Options Position**

**Futures Position for Delta Hedge**

Long on OTM 10,000 Call – 5 Lots

Short on Nifty Futures – 2 Lots

Total Delta of the Option – 0.40

Total delta of the Futures (- 1)

Total Delta Exposure (5X0.4) = 2 Deltas

Total Delta Exposure (2 X -1) = -2 Deltas

In the above case, the Delta Hedge gives a perfect hedge as the net delta in the above case is Zero. Thus the trader is now completely immune to any movement in pricing. This is one of the most important applications of Delta.

**Take a minute off for the sake of Gamma..**

Any discussion on delta will be in complete without a discussion on Gamma because while Delta measures the sensitivity, the gamma measures the acceleration. Technically speaking the gamma is the second derivative and measures the sensitivity of the option price to changes in delta. Gamma has a high relationship with volatility. When the volatility tends to be high, the gamma tends to be stable as a lot of value is already builtin to the time value. This is a useful input for options traders.

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