I want to calculate the 30/60/90/180 day 100% moneyness implied volatility for a stock. I think I know how to do it but would like to share my thought processes with the group to verify I'm on the right track. I roughly followed the process given in this white paper from Bloomberg (top hit for google search terms "bloomberg implied volatility calculation").
I'm going to run through an example using AAPL.
Assumptions:
- AAPL has European-style options
- As of 2016-04-29 compute the 60-day IV
- Stock closed at 93.75
- My calculations are correct :)
The process is as follows:
60-day IV would be for expiration as of June 28, 2016. Find option series bracketing that date. The June 17 and July 15 series both bracket it.
For each series, find 4 calls and 4 puts around 93.75. Two should be ITM, two should be OTM. This gives us the 90, 92.5, 95, and 97.5 strikes.
Compute cubic interpolation of a "synthetic" 93.75 strike for the calls and puts on both expiration dates.
June 17 Call, 3.1005
June 17 Put, 3.5855
July 15 Call, 4.0283
July 15 Put, 4.4095
- Compute the minutes to settlement from 2016-04-29T15:00:00 (CST) to the June 17 and July 15 dates.
June17_settlement = 70500
July15_settlement = 110820
60day_minutes = 86400
- Compute the time-weighted average using #4
June17 = (110820 - 86400) / (110820 - 70500) = 0.6057
July15 = (86400 - 70500) / (110820 - 70500) = 0.3943
Sanity check... 0.6057 + 0.3943 = 1.0
- Compute weighted average Call and Put prices for synthetic 60-day option
Call
(3.1005 * 0.6057) + (4.0283 * 0.3943) = 3.4663
Put
(3.5855 * 0.6057) + (4.4095 * 0.3943) = 3.9104
- Compute time to settlement for 60-day option
(60 / 365) = 0.1643835
- Use Black-Scholes to back out the IV of a Call and Put with stock price 93.75, strike 93.75, rfr 0.25%, time to maturity 0.1643835, and prices of:
Call(3.4663) = 22.7% IV
Put(3.9104) = 25.7% IV
Am I on the right path here? Any suggestions or corrections would be welcome.