The Heston stochastic volatility model for single assets and for asset portfolios: parameter estimation and an application to the Italian financial market

We investigate the performance of the Heston stochastic volatility model in describing the probability distribution of returns both in the case of single assets and in the case of asset portfolios. The R. parameters of the Heston model are estimated from observed market prices using a simple calibration method based on an integral representation of the exact probability density function of returns derived by Dragulescu and Yakovenko (2002). In the case of multiple correlated assets, the correlation parameters are obtained using a heuristic procedure based on a matrix completion algorithm. We present numerical experiments where several stocks traded on the Italian financial market are considered. We show that, both in the case of single assets and in the case of multiple correlated assets, the Heston model provides an excellent agreement with historical time series data and fits the empirical probability distribution of returns far better than the lognormal model.