# Calibration of Heston model

I would like to calibrate the Heston model and I am wondering which are the most common approaches used in the literature. Any suggestions (references from the main stream literature, notes or presentations) is greatly appreciated.

• Calibrate on a static vol surface, time series of returns, jointly on both, or something else? – Kiwiakos Apr 11 '16 at 19:20
• mainly on time series. – AlmostSureUser Apr 11 '16 at 19:33

• The main purpose is to clarify to student how the unknown component of the market price of risk and other parameters can be estimated on data. The model in the $Q$-measure reads as $$\left\{\begin{array}{lll} dS_t & = & r\,S_t\,dt+\sqrt{\xi_t}\,S_t\,dW^Q_{1,t}\\ d\xi_t & = & (k\,(\xi_0-\xi_t)-\eta\,\sqrt{\xi_t}\,\nu_{2,t})\,dt+\eta\,\sqrt{\xi_t}\,\,dW^Q_{2,t}\\ \end{array}\right.,$$ with $dW^Q_{1,t}\,dW^Q_{2,t}=\rho\,dt$. So by parametrizing $\nu_{2,t}=a\,\sqrt{\xi_t}$ one can derive the close form solution for the call option. How can the set of parameter $a,k,\xi_0,\eta$ be estimated? – AlmostSureUser Apr 13 '16 at 12:51