To: dxPrice subscribers
We continue to improve Theta calculation for expiring options. We will now use the extrinsic value of an option as an approximation for Theta on the day of expiration, which proves to be more accurate.
Technical details
Calculating Theta accurately is almost impossible on the day of expiration when using the Black-Scholes model. The calculated values tend to approach infinity and look confusing. To attain more precise values, we made an adjustment earlier this year.
Now we are continuing with another adjustment. On the expiration day, we will set Theta equal to the negated extrinsic value. So:
- When DTE > 1, Theta is calculated as usual
- When 1 ≥ DTE > 0, Theta equals minus extrinsic value
- When DTE ≤ 0 , Theta equals 0,
where DTE means days to expiration.
The reasoning behind this approximation is as follows: with DTE = 1 , the option can only lose its current extrinsic value and no more through the passage of time. Given that Theta is calculated as a one-day derivative, when DTE is less than or equal to 1 day, we set Theta to be equal to the negated current extrinsic value. When DTE is zero or negative, we set Theta to zero, as the option has already expired.
This approximation, although being empirical, has proven to be efficient. It will enable our clients to obtain more accurate Theta values on the expiration day.
Effective date
New logic will be rolled out on December 10, 2023. No actions are required from the clients.
Please refer to dxFeed Help Desk if you have any questions or concerns.