Can anyone give me a practical example of pricing and calculating IV on equity index options? (i.e. using real market data)

Question

I have been trading (mostly equity and equity index) options for a while now and I want to apply a slightly more quantitative approach to my trading - specifically, by calculating IV and incorporating it into my decision making process. BTW, I am referring to a "bog standard" BS model for exchange traded european and american options.

In most text books where IV is discussed, the sections that discuss pricing and IV calculation (on equity/equity index options) simply "pluck" the three key figures "out of the air" - the three key figures being:

1. Historical vol (in case of pricing)
2. Dividend yield
3. Applicable interest rate

HistVol

There are different ways of calculating historical volaltility, and as we all know, vol has a term structure. My question for histvol then is: Which methodology do practitioners use for estimating/calculating historical vol (and why?), and how does the calculation take into account the term structure of vol (vis-a-vie time to expiry for the option?)

Dividend Yield

It is impossible to obtain this data (for equity indices) from anywhere on the internet - without paying through the nose for it. Since I am a private investor, that rules that option out for me - does anyone know where I can obtain this data?. Failing that I would like to calculate the dividend yield from the equivalent total return index.

I think there must be a (constant?) relationship between:

i). a country's (annualized) interest rate ii). Dividend yield on an equity index in the country iii). Spread between the total return index and the 'adjusted' index

If my assumption is correct (maybe someone with an economics/finance background can help), how, may I calculate the dividend yield of an index from the above information - my objective is to derive historical dividend yields so that I can analyse historical option prices.

Interest Rate

Again, in books, the applicable interest is just "given". In practise though, one has to determine the applicable interest rate - presumably, by interpolating points on the relevant yield curve with the time to expiry. Could a practitioner please elaborate whether I am on the right path? - i.e. how the "correct" interest rate is obtained.

Answer 1

The "industry standard" for calculating implied volatility is OptionMetrics. Chapter 3 of their reference document contains details of how they calculate all the inputs to the standard Black-Scholes model. They also have a white paper just on dividend yield forecasting, which can potentially be a major issue.

However, much of the data they use is far from free or cheap, and they apply a considerable amount of effort cleaning and massaging the data before plugging into their models. This is why they charge so much for their service. There are other implied volatility providers that are cheaper, though (see What data sources are available online?).

Historical volatility is an entirely separate issue. As for how you should calculate HistVol, though, that depends on why you want to calculate it. It's a huge topic, best left to a new question.