# Introduction to Option Greeks

**Delta **

It is the amount an option price is expected to move with Rs.1 change in the price of the underlying stock. Calls always have a positive delta between 0 to 1. Put option always have a negative delta between 0 and -1. The delta will increase as the CALL option gets deeper in the money. The delta will decrease as the PUT option gets deeper in the money. The delta out of the money call and put options will get closer to zero as expiration approaches.

Example : Suppose if delta of call option = 0.65 ,and the stock goes up by Rs.1,in this case the price of call option will go up by Rs 0.65. Similarly if delta of put option = -.75 ,and the stock goes up by Rs.1 ,in this case the price of put option will go down by Rs 0.75

**Formula:**

*Delta = Change in price of derivative/ Rs. 1 change in underlying asset.*

**Gamma**

It is the rate at which the delta will change based on a Rs.1 change in the price of the stock. Options which have a high gamma means they are more responsive to the change in the price of the stocks.

High gamma is good in the case of an option buyer because as your option moves in the money, delta will approach 1 more rapidly. If you are an option seller and your forecast is incorrect, high gamma is really bad for you. That’s because it can cause your position to work against you at a more accelerated rate if the option you’ve sold moves in the money.

Example : In the above example if delta of call option when the stock has moved up by Rs.1 and the option subsequently moving up by Rs 0.65 the delta no longer remains at 0.65 it moves deeper in the money that is closer to 1,suppose now the delta of the call option is 0.80 ,so the gamma will be 0.15 (movement of delta from 0.65 to 0.80 )

**Formula:**

*Gamma = Change in delta /1 Rs. Change in the price of stocks.*

**Vega **

It is the rate of change in the option’s price (both call and put ) per 1% change in the implied volatility of the underlying stock. It tells how the implied volatility of a stock affects the price of the option on that stock. A drop in value of vega causes both call and put options to lose in values. When the value of vega rises , price of options increase and when the value of vega decreases, price of options decreases .

Example : Suppose we consider a call option with both strike and underlying at the same level (at the money) say Rs.90 and vega for this option is 0.4 ,this means that option price goes up by Rs. 0.4 if implied volatility increases by 1 point,and decreases by Rs. 0.4 when implied volatility decreases by 1 point .

**Formula:**

*Vega = Change in option price/change in implied volatility.*

**Theta**

Rate at which the option loses its value as the time decays. Since options lose value as expiration approaches, Theta estimates how much value the option will lose, each day, if all other factors remain the same. It is negative for both call and put option in case of an option buyer and positive in case of an option seller.

Example : For example, if an option is trading at Rs.75/- with theta of -1.5 then it will trade at Rs.73.5/- the following day (provided other things are kept constant).

**Formula:**

*Theta = Change in price of option /Time remaining to expiration.*

**Rho**

Rho measures the expected change in an option’s price per 1% change in interest rates. It tells you how much the price of an option should rise or fall if the “risk-free” interest rate increases or decreases. As interest rates increase, value of call options increase while value of put options will decrease.This is the reason that call options have positive rho and put options will have a negative rho.

Example :Suppose the current interest rate is 2% and Rho of a call option is 10 with its premium at Rs. 200. If the interest rate falls to 1%,the call option premium price goes down from 200 to 190 this Rs.10 change is called rho.

**Formula:**

*Rho = Change in option’s price /1% change in risk free interest rate.*

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