Historical Implied Volatility Calculation

Question

I'm trying to calculate implied volatility for the FTSE 100 for the last few years.

I have all the end of day data from LIFFE for the last few years. I have combined the data by weighting the implied volatilities for each strike by their volume traded and distance from the underlying close price. I then took the mean of the put and strike composite IVs.

However, The way I am currently calculating the data, I am always using the nearest expiry, and then moving on to the next expiry the next day, which is leading me to some fairly strange numbers. For example the day before the september expiry, IV was 40%, but the next day, when I start using the october expiry, volatility was down to 9%, which is clearly not true. I'm not sure if I should be using more than one expiry to calculate a days composite IV.

Here is what I get:

But I would expect something a bit more like this: https://www.google.com/finance?chdnp=1&chdd=1&chds=1&chdv=1&chvs=maximized&chdeh=0&chfdeh=0&chdet=1416609064419&chddm=113953&chls=IntervalBasedLine&q=INDEXEURO:VFTSE&&ei=Jb1vVOuPJ-SDwAPu24DoDQ

Thanks!

Answer 1

I'm not an equities guy so I don't know anything about volume-weighting, but if I was set this problem the approach that I would take would be to work out the implied volatility of each strike for that day, so that I have a graph of implied volatilty against strike, then interpolate on that graph to get the implied volatility for the ATM strike. Do that for every day and you have a time series of ATM implied vols. I hope that helps.

Answer 2

There is a big difference between a volatility index and taking the nearest expiration. Generally, a volatility index is considered a constant maturity. For instance, 30 day term. Since it is usually the case for listed options that there is not a 30 day option series, the index weights the two surrounding expiries. For instance, the 15 day and the 45 day.

Second, calculating implied volatilities on expiration day gets very irregular due to the very limited time left. Illiquidity and small price changes can wreck attempts to smooth implied vol. This gets especially bad as the day goes on. As you can imagine, the sensitivity of implied volatility to a 1c (or minimum price increment - tick) change gets very large with fractions of a day left.

This can be particularly devastating when calculating for a high volume strike that someone might be covering. Say an OTM option that a large seller needs to cover and may be willing to pay 5c when it is "worth" 1c to avoid undue risk going into expiration. This is ironic, of course, because generally it is the higher volume is considered the more accurate but it is the high volume that could be the distorting factor.

Thus, I give you the following potential remedies: 1) easy-peasy: stop calculating the surface on expiration day; end a day earlier. 2) harder, but not hard: update to a constant maturity index. You may want 30 days which is common but you may have reasons to choose another term. For instance, you are trading a strategy that uses 2-week options (or 3 month options).

There may be other, more appropriate answers depending on your purpose which you have not indicated.