For a buyer of the option the time always works against them because with each passing day the value of the option reduces. But, this same point is a major advantage for the seller of the option because the option's theta is a measurement of the option's time decay. The theta measures the rate at which options lose their value, specifically the time value, as the expiration date draws nearer. Generally expressed as a negative number, the theta of an option reflects the amount by which the option's value will decrease every day. Theta is popularly called time decay. Let us look at the table below:

Simulating Option Greeks on Reliance Industries 1100 Strike

Underlying Price

1110

Underlying Price

1110

Exercise Price

1100

Exercise Price

1100

Today's Date

27-11-2018

Today's Date

27-11-2018

Expiry Date

06-01-2019

Expiry Date

01-01-2019

Historical Volatility

20%

Historical Volatility

20%

Risk Free Rate

6.00%

Risk Free Rate

6.00%

Dividend Yield

1.35%

Dividend Yield

1.35%

DTE (Years)

0.11

DTE (Years)

0.10

Call Option

Put Option

Call Option

Put Option

Theoretical Price

37.5093

21.9411

Theoretical Price

35.2833

20.4087

Delta

0.5975

-0.4025

Delta

0.5984

-0.4016

Gamma

0.0053

0.0053

Gamma

0.0056

0.0056

Theta

-0.4582

-0.2785

Theta

-0.4831

-0.3033

Vega

1.4220

1.4220

Vega

1.3294

1.3294

Rho

0.6846

-0.5130

Rho

0.6022

-0.4465

Delta is the sensitivity of the option value to changes in Stock Price

Theta is the sensitivity of the option value to Time Decay

Vega is the sensitivity of the option value to changes in Volatility

In the above instance we have plotted the change in the value of the call option and the put option when there is fall of 5 days in the expiry. Let us assume that the time to expiry goes down from 40 days to 35 days. We can see the call value going up from Rs.37.5093 to Rs.35.2833. How do we determine to what extent this option will change? That is measured by Theta, which is a measure of time decay. In the above case, the Call Theta is (-0.4582). Let us now see how and to what extent the call value will change when the time to expiry drops by 5 days from 40 days to 35 days. The Call option price change will, therefore, be as under:

Old Option Value x Theta (Reduction in days to expiry)

This will give you the new value of the call option. The similar logic can be used for the put option. Remember that both call and put options lose value as they approach expiry so time decay hits calls and puts in a similar manner. The extent to which the option prices react to changes in the time to expiry is measured by the Theta.