What is option Theta and how to interpret it in practice?

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.