Difference between Black Scholes vs GARCH?

(Last Updated On: April 15, 2015)

Difference between Black Scholes vs GARCH?

Question from someone via my newsletter:

I have developed and implemented a method for computing volatility using  black&scholes with (strike, maturity, call prices, interest rate and constant return on asset), i have simulated data, my question concerning data : in general strike and maturity have a vector with 8 rows, so how can i use historical data to apply them for my method? for example concerning garch model we can compute the volatility using return of historical data then we estimate the parameter of model by maximum likelihood function.
this is the formula of volatility : sigma = sqrt( (dc/dt -(r-q)(c-k*dc/dk) /  k^2/2 d^2c/dk^2)
what is the difference between volatility of black scholes and volatility of Garch Model? is it the same result?
I am no math expert nor do I ever claim to be, I use Black Scholes to calculate an instrument’s implied volatility. I have not played a whole with GARCH at this point but appears to be something very different. Even in Matlab, they are both very different so check out their help for each.
Black Schole for IV:
http://www.mathworks.com/help/finance/blsprice.html
GARCH for forecasting as explained here:
http://www.mathworks.com/help/econ/cvm.forecast.html
Hope this helps
From Dr Paul Cottrell
BSM is an option pricing model utilizing a constant volatility methodology in its purest form. Practitioners use a moving window of volatility to update the BSM. A certain method to forecast out volatility is using a varying array of GARCH types. My books on forecasting and risk management cover this topic. In short, GARCH types are to forecast out volatility based on previous volatility. When solving for volatility for BSM, one gets the implied volatility to match to the current option price. IF you do not know the current option price one would have to use the “current” volatility or some average thereof.

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