Implied volatility calculator

Quote from freshpotato:

Hello,

I'm working on a implied volatility calculator for my new site, but are having some problems.

I have a rather lage options price database, and want to calculate implied volatility on all the options, does anyone have an idea on how to calculate iv?
More...

Hey Freshpotato,

When you google "black scholes" you'll get the primary formula. Plug in the market's actual price then run it backwards using the other measurable inputs and solve for the only remaining unknown, namely volatility. Under those circumstances, the volatility you will have calculated is IV. Google gives wikipedia. Try this site.

http://en.wikipedia.org/wiki/Black-Scholes


(Oh yeah, there is a much simpler formula than the million dollar black scholes and it gives functionally equilivant answers. I am just too lazy at this point in the evening to get the book out of my car and find the equation. sorry. maybe i'll dig deeper if you don't get a simpler answer than what you have so far. Basically speaking though, all models that try to price options have fundimental difficulities pricing the whole chain. Most are really only useful for the ATM options. Why? Because the most used models are based on Normal or Log Normal distribution of prices assumptions. The markets have much fatter and longer tails than these models account for. The sensiblilities (uh, ah nevermind) of the marketplace recognize this under pricing of OOM and moreso with WOOM options and in response, asks for additional premium charge. Thus the Nike Swoosh like IV Smile.)

You probably already knew this, and if so, I recognize that you likely know more than I do about options and their measurements. Always open to learn here. If I was being overly simplistic, please feel free to share more about your calculator. Thanks.

Peace and prosperity,
Lar
 
Quote from freshpotato:

Hello,

I'm working on a implied volatility calculator for my new site, but are having some problems.

I have a rather lage options price database, and want to calculate implied volatility on all the options, does anyone have an idea on how to calculate iv?

Best regards
More...

Freshpotato,

Did you get what you needed from Lar? For the IV using the Black-Scholes method, you're going to need:
  • The quoted option price.
  • The date/time of the quoted price.
  • The price of the underlying at the same moment as the option quote.
  • The "risk-free" rate of return at the time of the option quote.
  • Time remaining until expiry (that should be in your database already).
I think that is all for options (and futures, I think) on non-dividend paying stocks - plus the algorithm, of course. If you send me a private e-mail, I can send you an Excel implementation of Black-Scholes for computing the value of an options using implied volatility as an input. This may be useful for you to start with - perhaps you can reverse engineer it to distil out the IV from a known price.

However, note that if your historical database contains only closing options prices, then your results are going to be heavily skewed as options prices have a tendency to be skewed at the end of the trading day. If you have intra-day historical quotes, then it'll be brilliant!

I'm pretty sure that you did want an algorithm for IV, but some others are providing you with (incomplete) algorithms for SV (Statistical Volatility). For completeness:

All you need to do is compute the logarithmic change [ ln(p0)/ln(p1) : p0 = current period's close, p1 = previous period's close ] of the underlying's final price of the current period from the previous period, then compute the standard deviation of these log-changes over the number of periods you wish to report SV for. Since SV is typically reported as an annualized percentage, multiply by standard deviation above by the square root of the number of periods in a year. If the period you're using is days (very common), then this is nominally 252 trading days/year, (but 2008 has 253 in the US markets). Different sources of SV use different numbers here.

Typical samples to use are 30-day and 90-day SVs, which, non-intuitively use ~21 and 63 days respectively when computing the standard deviation. This is because a 'typical' 30 (90) calendar day period has 21 (63) trading days. Again, this actually changes from day to day, but for consistency, these values are often used. Some sources use 22 days/month.
 
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