Implied Volatilty Calculation

rower32 · April 28th, 2008, 8:56 pm

Hi, Is it possible to solve for the implied volatility if I am given the option price, spot price, strike price, maturity and the interest rate using B-S Model?? thanks

archishs2009 · April 29th, 2008, 2:45 am

There are many softwares and excel add-ins available to calculate the implied volatility given the various parameters of B-S model. I guess they use the unitary or newton-raphson method to get those answers. In fact why dont you try goal seek in excel?

Antonio · April 29th, 2008, 12:02 pm

I'm not sure what your question is exactly ?Do you know what implied volatility is ? (this is not a rude question, but if you can answer yes, then you can answer your question)

cemil · April 29th, 2008, 12:20 pm

Yes, you can calculate the implied vol of an option with BS model.It is easy to do.

andreikeda · April 29th, 2008, 12:32 pm

Yes, to calculate implied volatility, using the Black-Scholes method, you need:implied volatility (price of the option, strike price, spot price, time to matturity, interest rate)

Paul · April 29th, 2008, 5:27 pm

rower32 might be asking if you can write implied volatility as a nice (or even not so nice!) function of the other variables and parameters. In which case the answer is "no." You have to find implied volatility numerically as archishs2009 suggests.P

bilbo1408 · April 29th, 2008, 5:28 pm

bilbo1408 · April 29th, 2008, 5:29 pm

There is no closed form solution for it. You must use a numerical method. However, if you know the historical volatility used to calculate the theoretical value, the vega based on that value, and the current market price, it can be estimated by: vol - [(theoretical value - price)/vega].

rower32 · April 30th, 2008, 10:38 pm

Thanks for your answers!!!I used goal seek and got the results... however I was wondering if I could solve the equation by solving the whole B-S equation (mathematically) coming back from the option price, not by iteration. Obviously there's no way to do that I can't say I'm really good in math of the B-S model. I appreciate if you guys post a source that explains the proof step by step. antonio: that was a question for my derivatives class and I know what IV is, my only problem was the calculus of the model, but I'm working on it now.again many thx for replies

gjk77 · May 1st, 2008, 8:31 am

Peter Jackel has an excellent paper on the subject, "By Implication", wilmott magazine, 2006. Great approximation and advice on the numerical side of things. Maybe less well-known is a rational approximation in, Li, M., "You don't have to bother newton for implied volatility", 2006, ssrn.

GreekMartingale · May 3rd, 2008, 9:03 pm

fsolve in matlab works perfectly