Roberto Dieci Knihy

This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.

We provide a full analytical treatment of a multi-asset market model in which speculators have the choice between two risky and one safe asset. As it turns out, the dynamics of our model is driven by a four-dimensional nonlinear map and may undergo a transcritical, flip or Neimark-Sacker bifurcation. While the first bifurcation is associated with an undervaluation of the risky assets, the latter two may trigger (complex) endogenous dynamics. To facilitate our analysis, we first study a simpler two-dimensional setup of our model in which speculators can only switch between one risky and one safe asset.

We develop a model in which investors can participate in stock, bond and housing markets. Investors' market entry decisions are subject to herding e¤ects and depend on the markets' price trends and on their mispricings. The dynamics of our model is governed by a four-dimensional nonlinear map and its unique inner steady state is characterized by standard present-value relations between dividends, rents and the bond rate. Amongst other things, we show that endogenous stock and housing market dynamics emerge, countercyclical to each other, if investors react strongly to the markets' price trends. Such across feedback reflects investors' tendency to transfer their enthusiasm from one speculative market to another.

We combine a standard stock-flow housing market model, incorporating explicit relationships between house prices, the housing stock, and the rent level, with a parsimonious expectation formation scheme of housing market investors, reflecting an evolving mix of extrapolative and regressive expectation rules. The model results in a two-dimensional discrete-time nonlinear dynamical system. Based on realistic parameters, the model is able to generate endogenous boom-bust housing market dynamics with lasting periods of overvaluation and overbuilding. We thus exploit our model to investigate how real forces, in particular supply conditions, interact with expectations-driven housing market fluctuations.

We develop a novel financial market model in which the stock markets of two countries are linked via and with the foreign exchange market. To be precise, there are domestic and foreign speculators in each of the two stock markets which rely either on linear technical or linear fundamental trading strategies to determine their orders. Since foreign stock market speculators require foreign currency to conduct their trades, all three markets are connected. Our setup entails a natural nonlinearity which may cause persistent endogenous price dynamics. Moreover, we analytically show that market interactions can destabilize the model’s fundamental steady state.

We develop a simple model of a speculative housing market in which the demand for houses is influenced by expectations about future housing prices. Guided by empirical evidence, agents rely on extrapolative and regressive forecasting rules to form their expectations. The relative importance of these competing views evolves over time, subject to market circumstances. As it turns out, the dynamics of our model is driven by a two-dimensional nonlinear map which may display irregular boom and bust housing price cycles, as repeatedly observed in many actual markets. However, we also find that speculation may be a source of both stability and instability.