Abstract:
This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of U.S. stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behavior in the second half. Translating the results, we find that the U.S. stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, the exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.

Keywords: stochastic cusp catastrophe model, realized volatility, bifurcations, stock market crash

JEL codes: C01, C53

Download here: http://dx.doi.org/10.1080/14697688.2014.950319

Keywords: heterogeneous agent model, behavioural finance, herding, overconfidence, market sentiment, stock market crash

JEL codes: C1, C61, D84, G01, G12

Abstract:
The main aim of this work is to incorporate selected findings from behavioural finance into a Heterogeneous Agent Model using the Brock and Hommes (1998) framework. Behavioural patterns are injected into an asset pricing framework through the so-called ‘Break Point Date’, which allows us to examine their direct impact. In particular, we analyse the dynamics of the model around the behavioural break. Price behaviour of 30 Dow Jones Industrial Average constituents covering five particularly turbulent US stock market periods reveals interesting patterns in this aspect. To replicate it, we apply numerical analysis using the Heterogeneous Agent Model extended with the selected findings from behavioural finance: herding, overconfidence, and market sentiment. We show that these behavioural breaks can be well modelled via the Heterogeneous Agent Model framework and they extend the original model considerably. Various modifications lead to significantly different results and model with behavioural breaks is also able to partially replicate price behaviour found in the data during turbulent stock market periods.