InvestorQ : What is option Theta and how to interpret it in practice? # What is option Theta and how to interpret it in practice? Answer 3 years ago
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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.
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