Saturday, April 27, 2013

The actual time decay Chart of OTM option Theta and Vega

I'm interested to understand the real time-decay of my high probability option selling monthly income portfolio. I tried to use the TOS software without success, since it's designed to show the Greeks of various strike prices mainly. The ThinkScript has some bugs that prevent me from writing a script to display the time decay for every trading day. If ThinkOrSwim can fix the bugs, I may be able to design such a script for TOS chart.

For now, it's possible to display Theta and Vega hourly chart for a single option. So I used a sold SPX May put as the initial example which is shown below. The TOS chart also has a bug that prevent me to display it in daily chart. I had to use intraday (4 hour is selected to present more data) chart for this purpose.
As we can see from the chart, the sold put kept losing value as time passed by and SPX rose. It's apparent that Vega kept losing value as time passed by. It also reacted inversely to the SPX price (in the same direction as IV). My goal is to display implied volatility and Vega's impact on option values. Unfortunately, the IV functionality in ThinkScript is not working. I'm waiting for a response from TOS tech support to see if they are going to fix these type of issues.

The Theta time decay ((32.5-25)/32.5 = 23%) in last month was not that much when compared with that ((170-57)/170 = 66%) of the Vega. The Theta's reaction to SPX's price is similar as Vega: a reverse relationship with price (direct relationship with IV). Theta peaked on 2nd last Thursday as that was the lowest price day of SPX in the period. At the same day, the put option price also had a smaller peak to the market sell-off.

It looks to me an iron condor with negative Vega would benefit more time decay than a double calendar which has positive Vega if the spreads are opened two months before expiration. Is it really true? I'll have to analyze it in a future post.

What it really matters is that the put option price has been falling down since the open date. This is the ultimate effect of all Greeks. I'll continue to monitor the option price drop till the expiration day to get a overall picture of the option time decay.

Update: Since this post is becoming one of the popular ones of my blog, I'd like to update additional thoughts here.
1. As shown in the top section of the graph, it's apparent that Delta or index price changes have the most significant impact on option prices. The sold put option is out of the money, so the option price is made of time value solely. Using a moving average of the option price in the chart may better illustrate the decay of time value. I can do that in a future post.
2. Option Theta value becomes larger as the option price increases. But the percentage of Theta over time value may change different. I will create a ThinkScript to track the Theta value as a percentage of time value in a future study as well.


  1. More than 6 months later after the post, I took another look at the Theta of the sold put option time decay chart again.
    On the 1st Monday: SPX=1520/Theta=32
    On the 5th Monday: SPX=1552/Theta=38
    So the sold put Theta INCREASE for this 5 weeks is 6 while SPX increased over 30 points. In this particular case, Theta reached its peak at the 5th week before expiration (4-12). In theory, Theta was supposed to keep increasing (if stock price stayed the same) as expiration approaching. But it did not (actually fell significantly) because the stock price rose in the real market.

  2. hello, any update on this post? very interesting