Another study of option implied volatility and its time decay

After my recent discovery of the volatility discrepancy in TOS analyzer, I started investigating the IV of options. In one of my post, I have showed a chart illustrating the time decay of Vega. This weekend, I further studied the time decay of implied volatility and would like to note down and share with readers.

Implied volatility is always associated with a time frame. For the composite IV of options (IV of all option chains and expiration , the time frame is 1 year of trading days. It's annualized. To estimate the IV of an individual option which has a definite life time, we can calculate the daily IV first, then multiply it by the remaining trading days to derive the actual IV of the specific option.

The daily IV = Annualized IV / square root of 256 trading days = IV / 16 in brief.

Therefore, the IV of an individual option = daily IV x square root of trading days to expiration.

Based on the above approximation, it's easy to understand that as days pass by, the IV of each option gets smaller and smaller.

Also note that the individual option's IV is directly proportional to the square root of trading days. At intraday time frame of trading, market makers will adjust the IV continuously. If other influencing factors do not change, the option's IV will decrease from market open to close. This is the intraday time decay, specially big for weekends as noted for option Theta before. In fact, Vega has very similar characteristics as Theta with the exception that IV can change in two directions (up and down) and time can only elapse.

We often use $VIX (CBOE volatility index) as a measure of overall market IV. It's actually derived as the IV of a hypothetical 30-day option of SPX using a weigthed average of two nearest expiration series. The time frame associated with VIX is 30 days here. For option trades that use two month back options, the volatility could be square root (2x22) x IV/square root(22) = 1.41 x IV which is significant bigger.

Unfortunately, TOS does not offer the feature to display IV decay over time for individual options at the moment.