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.
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.
In the above example with every 1 point change in the index the price of the option will change by Rs 0.45. When we actually change the spot price by 1 point keeping all other parameters same, we find that the call option price has gone up by Rs 0.44. As you can see there is a slight deviation, but this is normal.
Note that the delta changes with movements in the underlying stock or index and time to expiration and therefore the value would be continuously changing.
As shown in the example with every 1-point change in the index at 1,070.1 the delta is Rs 0.45. However, this Rs 0.45 will change by Rs 0.0085, with every incremental change in the index by one point.
Gamma is the same for calls and puts.
Theta is usually negative for an option as with a decrease in time, the option value decreases. This is due to the fact that the uncertainty element in the price decreases.
In the example, the number of days has decreased by 1 therefore, this comes to about 0.2762% of a year (1/365). Therefore, the change of 1 day (decrease by 0.2739% of a year), the option value should change by 352.527*0.002739 = 0.97383. This is assuming there is no other change in the parameters.
Vega is the measure of an option’s sensitivity to changes in the volatility of the underlying asset.
Vega (sometimes known as kappa) is the change in option price given a one-percentage point (1%) change in volatility of the index or stock.
In the example, when the volatility has been changed from 25.1% to 26.1% the price of the stock options has gone up by Rs 0.73. The value of Vega is 74.09, which means the price should go up by Rs 0.74 for every 1% increase in volatility.
It can also be interpreted as: if the volatility changes by a small amount, then the option value should change by 15.88 times that amount. If the volatility increased by 0.01 (from 25.1% to 26.1%), then the option value should change by 74.09*.01 = 0.7409.
The value of Vega is same for put and call options.
Here the value of Rho is 14.10. This has to be interpreted as if the risk free interest rates go up by 1% the price of the option will move by Rs 0.14109. In the example we see that when the interest rate increases by 1% the price increases by Rs 0.13895.
To put this in another way: if the risk-free interest rate changes by a small amount, then the option value should change by 14.10 times that amount. For example, if the risk-free interest rate increased by 0.01 (from 10% to 11%), the option value would change by 14.10*0.01 = 0.14.
For a put option the relationship is inverse. If the interest rate goes up the option value decreases and therefore, Rho for a put option is negative.