Since option price changes with underlying stock due to the impact of Delta, I decided to observe the option premium decay after taking out the Delta-induced option price changes. The option time value in my study was restricted to changes due to volatility (Vega) and Theta mainly in this way:
Option time value = extrinsic value =
previous price + Delta-induced change + sum of Vega and Theta induced changes.
Using a simple approximation of Delta-induced option price changes, I was able to chart the Delta-adjusted time decay curve of the naked put which took out the Delta-induced change in the above equation. The directional price change from Delta is calculated as shown below using ThinkScript:
plot TmValExclDelta = extrVal - ((absValue(Delta()) + gamma() * opChange)/2) * (opChange);
The entire script is downloadable for anyone who is interested. It can be used as a base for other option premium analysis. The resulted chart is downloadable in a PDF file if anyone needs to see a clearer picture.
As shown in the above chart, I found a few key points below. I think a picture is worthless a thousand words. There are other points that can be observed from it as well. Note the left vertical axis is FXI ETF price and right vertical axis is FXI Dec$37.5 put option price.
- The FXI option price was high while its time value was low as FXI dropped below the strike price.
- The FXI option time decay acceleration started at about 2.5 months before expiration.
- The naked put sold at Delta around 0.3 and its time decay stayed close to the bottom downtrending line as FXI price consolidated for 3 weeks.
One of the interesting point to me is that this option started rapid decay around 2.5 months. If one sells the option on 2.5 months before expiration and exit it at around 1 month before expiration, he would capture a good amount of premium values with relatively smooth time decay as well.