Calibrating the Heston Model to Option Prices in MATLAB
Summary
The document presents a MATLAB workflow for calibrating Heston stochastic-volatility parameters to option data. It prices calls by numerically integrating two probability terms, then uses a bounded nonlinear least-squares fit to minimize price errors scaled by the square root of the bid-ask spread. The fitted variables are transformed into the model parameters reported as the solution.
The material is an example implementation and a troubleshooting question: the author reports that MATLAB returns an empty result but gives no diagnosis or successful calibration evidence. It therefore illustrates the intended objective function, input data layout, and parameter bounds without establishing that the code runs correctly. Readers should treat the implementation as unverified; the document does not discuss numerical stability, integration accuracy, data quality, or how to identify the cause of the empty output.
Key ideas
- The example prices European calls with a Fourier-style integral for the Heston model.
- A bounded least-squares routine fits parameters to observed option prices.
- Price residuals are scaled using the bid-ask spread as a measure of quote uncertainty.
- The author reports an empty MATLAB result, but the document provides no fix or validation.
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Full text
# MatLab code does not work for Heston model calibration
# MatLab code does not work for Heston model calibration
I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does somebody know what's wrong with this code? Thanks in advance.
```
function call = HestonCallQuadl(kappa,theta,sigma,rho,v0,r,T,s0,K)
warning off;
call = s0*HestonP(kappa,theta,sigma,rho,v0,r,T,s0,K,1) - K*exp(-r*T)*HestonP(kappa,theta,sigma,rho,v0,r,T,s0,K,2);
function ret = HestonP(kappa,theta,sigma,rho,v0,r,T,s0,K,type)
ret = 0.5 + 1/pi*quadl(@HestonPIntegrand,0,100,[],[],kappa,theta,sigma,rho,v0,r,T,s0,K,type);
function ret = HestonPIntegrand(phi,kappa,theta,sigma,rho,v0,r,T,s0,K,type)
ret = real(exp(-i*phi*log(K)).*Hestf(phi,kappa,theta,sigma,rho,v0,r,T,s0,type)./(i*phi));
function f = Hestf(phi,kappa,theta,sigma,rho,v0,r,T,s0,type);
if type == 1
u = 0.5;
b = kappa - rho*sigma;
else
u = -0.5;
b = kappa;
end
a = kappa*theta; x = log(s0);
d = sqrt((rho*sigma*phi.*i-b).^2-sigma^2*(2*u*phi.*i-phi.^2));
g = (b-rho*sigma*phi*i + d)./(b-rho*sigma*phi*i - d);
C = r*phi.*i*T + a/sigma^2.*((b- rho*sigma*phi*i + d)*T -2*log((1-g.*exp(d*T))./(1-g)));
D = (b-rho*sigma*phi*i + d)./sigma^2.*((1-exp(d*T))./(1-g.*exp(d*T)));
f = exp(C + D*v0 + i*phi*x);
function ret = HestonCallDifferences(input)
global NoOfIterations; global NoOfOptions; global PriceDifference;
NoOfIterations = NoOfIterations + 1;
%counts the no of iterations run to calibrate model
for i = 1:NoOfOptions
PriceDifference(i) = (OptionData(i,5)-HestonCallQuadl((input(1)+input(3)^2)/(2*input(2)),input(2),input(3),input(4),input(5),OptionData(i,1),OptionData(i,2),OptionData(i,3),OptionData(i,4)))/sqrt((abs(OptionData(i,6)-OptionData(i,7))));
%input matrix = [kappa theta sigma rho v0]
end
ret = PriceDifference';
end
clear;
global data; global OptionData;
NoOfIterations = 0;
[data,text]=xlsread('OptionData.xlsx');
%OptionData = format [r-q,T,S0,K,Option Value,bid,offer]
Size = size(data);
NoOfOptions = Size(1);
OptionData = data;
%input sequence in initial vectors [2*kappa*theta - sigma^2,theta,sigma,rho,v0]
x0 = [1 0.5 1 -0.5 0.5];
lb = [0 0 0 -1 0];
ub = [20 1 5 0 1];
options = optimset('MaxFunEvals',20000);
%sets the max no. of iteration to 20000 so that termination doesn't take place early.
tic;
Calibration = lsqnonlin(@HestonCallDifferences,x0,lb,ub);
toc;
Solution = [(Calibration(1)+Calibration(3)^2)/(2*Calibration(2)), Calibration(2:5)];
```Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.