# What is a canonical reference on calibrating the Heston Model?

I am trying to calibrate the Heston model (or another stochastic volatility model).

I read about maximum likelihood estimates, but there are so many articles as well with other algorithms.

Can you suggest an article (from https://papers.ssrn.com/) which explains a relatively easy algorithm that is applied nowadays.

• What do you want to calibrate the model to -historical returns or option prices? – LocalVolatility Nov 6 '16 at 11:23
• I want to know the parameters (kappa, lambda and to on) So there is a distinction between using option prices and historical data? I was thinking option data, since Dupire's model also uses this. – Emily Nov 6 '16 at 11:50
• @Emily - yes, it depends on whether you are interested in obtaining a Heston dynamic under the physical measure $\Bbb{P}$ (calibration to historical time series) or under the risk-neutral measure $\Bbb{Q}$ (calibration to option prices). The techniques are not the same. – Quantuple Nov 6 '16 at 12:05
• Thanks @Quantuple Let's assume to Q (so using option prices) Do you have a suggestion for a clear and good algorithm? – Emily Nov 6 '16 at 12:22
• @LocalVolatility Option prices – Emily Nov 6 '16 at 12:22

There are so many articles in this context, such as

1. Estimating using loss function

This method uses the error between quoted market prices and model prices, or between market and model implied volatilities . You can consider these article

2.Differential evolution

Vollrath has applied the algorithm to interest rate and option model and has found the algorithm effective in identifying the global minimum in the parameter space, albeit at the expense of high computation time. You can this method in this article

3.Maximum likelihood estimation

Atiya and Wall (2009) show how to obtain the maximum likelihood estimates of the physical parameters of the Heston model using a time series of historical stock prices.

• Also you can see it: quant.stackexchange.com/questions/18400/… – user16651 Nov 6 '16 at 17:38
• Looks like we have a specialist here. – SRKX Nov 7 '16 at 5:48
• +1 - To add to this very nice answer: For a calibration to vanilla option prices, on a pure computational side, I really encourage you to use a single integral form for the European call/put price (i.e. not the standard Heston formulation with its 2 separate integrals, but rather formulations à la Attari/Lewis/Joshi) and to cache evaluations of the characteristic function. See here: frankfurt-school.de/clicnetclm/…. Also be sure to use a formulation of the char. fun. which avoids branch cuts in the complex plane (see "little heston trap") – Quantuple Nov 7 '16 at 8:55
• @Quantuple Thanks . You are right. little Heston trap reduce discontinuities and oscillations of integrand . – user16651 Nov 7 '16 at 15:18