Prospect Theory in the Heterogeneous Agent Model

Using the Heterogeneous Agent Model framework, we incorporate an extension based on Prospect Theory into a popular agent-based asset pricing model. This extension covers the phenomenon of loss aversion manifested in risk aversion and asymmetric treatment of gains and losses. Using Monte Carlo methods, we investigate behavior and statistical properties of the extended model and assess how our extension is manifested in different strategies. We show that, on the one hand, the Prospect Theory extension keeps the essential underlying mechanics of the model intact, but on the other hand it considerably changes the model dynamics. Stability of the model is increased and fundamentalists may be able to survive in the market more easily. When only the fundamentalists are loss-averse, other strategies profit more.

     

Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

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 theory 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 US 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 behaviour in the second half. Translating the results, we find that the US 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, 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.