Delta And Volatility

Next, we will learn Delta with respect to change in volatility:

Changes in volatility will change Delta. Even though the stock price doesn’t move, Delta will change when there are changes in volatility. However, for the ATM options, the Delta is relatively unaffected to changes in volatility. This means ATM options will have Deltas close to 0.5 (assuming other factors are constant).

Let’s look at the table given below where Spot is 17500 and days to expiry is 14.

AT THE MONEY STRIKE 17500

Observations: As Volatility decreases,

Both Call and Put premium decreases.
Call Delta and Put Delta both approach 0.5 and -0.5 respectively.

Let us figure out the same for ITM/OTM strikes. First let us take a strike, here the call option is ITM and obviously the put option for the same strike is OTM.

STRIKE 17000 where call option is ITM and put option is OTM

As volatility decreases, both Call and Put premium decreases. However,

ITM Call Option approaches to 1.
OTM Put option approaches to 0.

Now let us calculate the same for the strike where Put option is ITM and call option is OTM.

STRIKE 18000 where call option is OTM and put option is ITM

The observation here is the same that both call and put option premium decreases with a decrease in volatility. Just now the call option is OTM, so its delta approaches 0 while, Put option being ITM, its delta approaches -1.

We see that in contrast to the ATM, the ITM or OTM option Delta is more sensitive to changes in volatility.

Lastly, let’s try to figure out the relationship of Delta with respect to the Rate of Interest.

Assuming spot to be at 17500 and taking ATM options, days to expiry 14 days and volatility to be 17%.