Volatility of price indices for heterogeneous goods

Christian Hafner (UCL, Belgien)
Wednesday, November 30, 2011 - 10:00am
Weierstrass-Institut, Erhard-Schmidt-Raum

Hedonic regression is a common tool to estimate price indices and has been widely used to construct price indices of markets with heterogenous goods. Two prominent examples are the real estate and the art market. Although some efforts have been made to improve the efficiency of parameter estimates, there is no systematic treatment of volatility in these markets. Considering heterogenous goods as alternative investments, this lack of reliable volatility measures prevents an objective assessment of investment opportunities based on classical mean-variance criteria. Moreover, derivatives on subsets of the traded goods require a precise estimation of the underlying volatility. For example, in art markets, auction houses are interested in derivatives for collections or individual art objects in order to hedge their risks. In this paper we propose a new model which explicitly defines an underlying stochastic process for the price index. The model can be estimated using maximum likelihood and an extended version of the Kalman filter. We derive theoretical properties of the volatility estimator and show that it outperforms the standard estimator. To illustrate the usefulness of the model, we apply it to a large data set of international blue chip artists. (joint work with Fabian Bocart)