Option theta explainedOption theta is a mathematical tool used to capture how the price or a value of an option reacts to time, specifically how it changes as the option approaches its expiration or maturity date. Put-call parityPut-call parity is a financial relationship between the price of a put option and a call option. Option theta is also often called time decay which means exactly what it says.An option has some value right at the moment when it is written. As the option approaches its expiration date, the option time value decreases, or we can say it "decays." However, the time value does not diminish linearly. Option theta is negative because the relationship between option's value and the time to expiration is inverse.

As the option ages, the time value decreases.When thinking about the size of the option theta, it is however easier to think in terms of option theta absolute value. Option theta is the lowest (or the highest when looking at its absolute value) when an option is at-the-money.

When an option is completely worthless or very valuable, then the absolute value of the option theta is minimal.Let's use a call option as an example.

When you have a call option that is deeply in the money, then it already is in-the-money, and just mere ageing of the option does not hurt it as much as it would hurt an option that is on the verge of being in- or out-the-money.This relationship is in a way similar to two other option sensitivity indicators. As the option gets closer to its expiration date, it tends to loose its time value more quickly. Having 90 days to the expiration date, an option changes its value (assuming other factors are constant) from the 90th day to the 89th day only minimally.

We can express this schematically using the following equation:,where dV is the value of an option and dT is the time to expiration.

Option delta and option gamma measure option sensitivity to changes in the price of the underlying asset. Option vega measures option sensitivity to the volatility of the price of the underlying asset.

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