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Would anyone have a code (pref. Matlab or R) for any type of estimation (QML, GMM) not using option prices of a stochastic volatility model driven by a CIR process described below?

\begin{equation} dS_t = \mu dt + \sqrt{v_t} dW_t^1 \end{equation} \begin{equation} dv_t = \kappa (\theta - v_t) dt + \sigma \sqrt{v_t} dW^2_t \end{equation} such that $dW_{t}^{1}\,dW_{t}^{2}=\rho dt$

I just need to cross-check my results.

Thanks!

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  • $\begingroup$ That's the Heston model. You will find plenty of information on this site and also implementations on Google. Plus, in R it's already implemented (packages fOptions and NMOF). Remember that the Heston model models also the correlation between the two Wiener processes. $\endgroup$
    – Arrigo
    Dec 23, 2014 at 10:52
  • $\begingroup$ @Arrigo: Thanks, there's been a typo in the price process specification. Unlike for Heston, I need to estimate without using the option prices. $\endgroup$ Dec 23, 2014 at 11:16
  • $\begingroup$ Here it is! Heston calibration in Matlab $\endgroup$ Dec 23, 2014 at 12:52
  • $\begingroup$ Answers should contain enough information to actually answer the question. A simple link to another site should just be a comment. $\endgroup$ Dec 23, 2014 at 14:08
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    $\begingroup$ @GabrielePompa thanks. but this is not a heston model (doesn't assume dependency between the wieners) + for calibration of the heston option prices are needed, which i do not have. $\endgroup$ Dec 23, 2014 at 16:37

1 Answer 1

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  1. Purpose:
    • CIR process maximum likelihood estimation.
  2. Input
    • Model.Data = Time series of interest rates observations.
    • Model.TimeStep = Delta t; recommended: 1/250 for daily data and 1/12 for monthly data.
    • Model.Disp = 'y' | 'n', (default: 'n').
    • Model.Method = 'ncx2pdf' | 'besseli' (default: 'besseli').
    • Model.MatlabDisp = 'off' | 'iter' | 'notify' |' final' (default: 'off').
  3. Output:
    • Results.Params = Estimated parameters (kappa, theta, sigma).
    • Results.Fval = Objective function value.

function Results = CIRestimation(Model)
Nobs = length(Model.Data);
r = Model.Data(1:end-1);
dr = diff(Model.Data);           
dr = dr./r.^0.5;
regressors = [Model.TimeStep./r.^0.5, Model.TimeStep*r.^0.5];
drift = regressors\dr;
res = regressors*drift - dr;
alpha = -drift(2);
theta = -drift(1)/drift(2);
sigma = sqrt(var(res, 1)/Model.TimeStep);
InitialParams = [kappa theta sigma];
if ~isfield(Model, 'Disp'), Model.Disp = 'y'; 
end;
if strcmp(Model.Disp, 'y')
    fprintf('\n initial kappa=...%+3.6f\n initial theta=...%+3.6f\n initial sigma = %+3.6f\n',kappa, theta, sigma);
end
if ~isfield(Model, 'MatlabDisp'), Model.MatlabDisp = 'off';
end;
options = optimset('LargeScale', 'off', 'MaxIter', 300, 'MaxFunEvals',300, 'Display', Model.MatlabDisp, 'TolFun', 1e-4, 'TolX', 1e-4, 'TolCon', 1e-4); 
if ~isfield(Model, 'Method'), Model.Method = 'besseli'; 
end;
if strcmp(Model.Method, 'ncx2pdf')
    [Params, Fval, Exitflag] =  fminsearch(@(Params) CIRobjective2(Params, Model),InitialParams, options);   
else
    [Params, Fval, Exitflag] =  fminsearch(@(Params) CIRobjective1(Params, Model),InitialParams, options);   
end   
Results.Params = Params;
Results.Fval = -Fval/Nobs;
Results.Exitflag = Exitflag;

if strcmp(Model.Disp, 'y')
    fprintf('\n kappa = %+3.6f\n theta    = %+3.6f\n sigma = %+3.6f\n',...
        Params(1), Params(2), Params(3));
    fprintf(' log-likelihood = %+3.6f\n', -Fval/Nobs);
end

end

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