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Options Theta

Theta, the time value of options or the measure of time decay

Definition: It is a measure of the daily dollar amount an option will theoretically gain/lose for each one day change in time to expiration.  It is also called the extrinsic value of the option as time is external or independent from the behaviour of the underlying.

Theta‘s behaviour is dictated by the pricing model such as the Black-Scholes formula or its variants:

  • ATM options have the most Theta and it increases as expiration approaches.
  • ITM/OTM options have less Theta and it decreases as expiration approaches.

Option ThetaOptions decay at the Square Root of time (days) and at different rates for in (ITM), out (OTM), and at the money (ATM).  It is higher on longer term options but is a larger percentage of price on near-term options.

  • The entire extrinsic value is exposed to time decay, which will, all else held equal, reduce the value of an option every passing day.
  • Long options will have Negative Theta, meaning they are losing value over time.
  • Short options will have Positive Theta, meaning they are gaining value over time.
  • The amount of time decay will increase as the option approaches expiration.
  • An option has no time value at expiration and is only worth its intrinsic value.
  • Theta is generally linked to Vega i.e. higher Vega leads to higher Theta.

For instance, if a Call option is quoted $2.19 it will actually cost $219 to cover 100 underlying.  Assuming its Theta is $6, then a time decay of $6 will apply for each passing day.   Along with Implied Volatility (IV), Theta is an essential part of OM’s options strategy which combination is a net seller of Puts and Calls in order to capture Theta.

theta
Frightening Theta Calculations

 

Above you can see the theoretical formula for Theta…  Needless to say that one should leave it to a good options analysis software, or at the very least a spreadsheet calculator (e.g. Hoadley).  Rest assured; no options practitioner, hobbyist or professional ever goes back into this kind of maths themselves.


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