In the last tweet thread, we talked about Options Greek Gamma. In this tweet thread, we will talk about an important Options Greek 'Theta' denoted by (Θ)
An option's value is comprised of two components – intrinsic value &extrinsic value (also called time value). As time passes, the time value portion of the option gradually depreciates until expiry and at expiration the option value worth is exactly equal to the intrinsic value.
Assuming other conditions are constant, the more time left in the life of an option, the more valuable it is as there is more time for the underlying to make a move. As the life of the option decreases, so does the time value of the option.
The rate at which the value of the option depreciates as time passes, assuming all other conditions remain unchanged, is called Theta or time-decay and denoted as θ.
Theta is usually expressed as the value lost by the option with each passing day. Theta can also be defined as the rate of change in the option’s price per unit change in the time to expiration (a day in our case).
Theta can act as a double-edged sword and it can be a good thing or bad thing depending on the option position. Theta hurts the long option positions due to time-value depreciation whereas it aids the short option positions due to accrual of theta portion of the profit.
A long option position has a negative theta as it loses value with the passage of time, whereas a short option position has a positive theta as it gains with the passage of time.
For example, as shown in the figure below, the 28MAY2020 expiry ATM option call (9000CE) has a theta of rupees -1160. It means, at that instance, assuming other conditions remain constant, the option loses the value of rupees 1160 every passing day. 
Just like other option Greeks, theta also changes and is not a constant. Moneyness, time to expiration, and volatility of the option all affect the theta of the option.
Theta of an option will vary depending on not only market conditions but also on its moneyness that is whether it is in-the-money (ITM), at-the-money (ATM), or out-of-the-money (OTM).
As shown in the figure below, Theta is greatest for option when it is ATM and decreases when it is ITM or OTM.
The time value of an option is a direct function of the extrinsic value that the option possesses. Because ATM options have the highest time-value (or extrinsic value), they have higher thetas, whereas the OTM & ITM options have lower time-value, and therefore have lower thetas.
The days to expiration have a direct relationship to theta. During the early life of an option, the rate of time-value decay is similar for all options. But as the expiration approaches, the rate of decay slows down for the ITM & OTM options while it accelerates for ATM options.
This can be attributed to high extrinsic value left in the ATM options while low or negligible extrinsic value left in ITM & OTM options. In the figures below, see the different thetas of a long-dated ATM option (June2020 Expiry) and closer to expiry ATM option (May2020 Expiry).
Volatility has a direct effect on theta. When volatility is high, there is uncertainty in the market & options have high premiums. As a result, options have a higher extrinsic value & therefore will have higher thetas compared to the same options under low volatility conditions.
See the figure below to understand the direct effect of volatility on both premium of the options as well as the thetas.
