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Does anyone know of a beginners guide to setting up or solving the problem:argmin Sum( (Cstar - Cobs)^2)(theta)where Cstar is estimated and Cobs observed option prices. I'm having a bit of a problem on how you actually input estimated option prices in order to solve for the parameters. I have a number of ideas, but imagine there is a trick to it I'm just not seeing.Thanks in advance,Keith

Cstar comes from a model. Each model has a -set- of unknown (unobserved) parameters (your theta), thatare being estimated.For example, if the model is Black-Scholes, there is only one unobserved parameter: sigma.The result of the minimization will be a sort of mean sigma (implied volatility) across your set of actual option prices.If the model is the Heston model, there are 5 parameters that need to be found.In general, you code a model formula and a minimization routine, which both take the N unknown parametersas arguments [plus a whole bunch of known parameters as additional arguments]:Cstar = CModel(parameter1, parameter2, ...., parameterN, {Known parameters, Strike Price, dividends, etc} ).Then, you make a starting guess at the parameters, and after running a while, the minimizationroutine will, if you are lucky, converge at a (local or global ) minimumparameter1*, parameter2*, ...., parameterN*It's not especially easy to get right, so be prepared to spend a lot of time on it.regards,

The choice of optimization method depends somewhat on the model you're trying to fit. Also, what language are you using? In MATLAB the function fminsearch works well for a lot of models.