Calibrating a Market Fraction Model to the Power-law Behaviour in the Dax 30

Bounded rationality and heterogeneity have been developed in the recent asset pricing literature to explain complicated market behaviour, such as market booming and crashes, and various stylized facts in high frequency data, such as fat tails, volatility clustering and power-law behaviour in returns, which are difficult to be explained by the standard asset pricing theory based on rational expectations and representative agent paradigm. Guided by theoretical analysis, numerical simulations of those structure models have demonstrated a great success to generate and explain most of these stylized facts. However calibration of these heterogeneous agent models to the most of these stylized facts, in particular fat tail in return distribution and longrange dependence in return volatility, seems difficulty so far. This paper calibrates the simplest market fraction asset pricing model of fundamentalists and trend followers we have developed recently to the power-law behaviour of the DAX 30. With the parameter values of the calibrated model, we show that the autocorrelations (of returns, the absolute returns and the squared returns) of the market fraction model share the same pattern for the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviors and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the calibrated market fraction model match closely to the corresponding estimates for the DAX 30. The results strongly support the explanation power of the heterogeneous agent models. JEL Classification: C15, D84, G12 CALIBRATING THE POWER-LAW BEHAVIOUR IN THE DAX 30 3