Asset price dynamics with small world interactions under hetereogeneous beliefs

We propose a simple model of a financial market populated with heterogeneous agents. The market represents a network with nodes symbolizing the agents and edges standing for connections between them, thus, embodying local interactions in the market. By local interactions we mean any kind of interplay between the decisions of the agents unaffected by the market mechanism and unrelated to the physical distance between the agents. Using the rewiring procedure we restructure a network from regular lattice to random graph by varying the probability of the agents to switch from one trading strategy to another. We study how the network structure influences the asset price dynamics. The results show that for some intermediate values of the probability to switch, corresponding to a small world network, the price dynamics become reminiscent to the real. While for the boundary values of the probability the dynamics lacks some typical features of the real financial markets.local interactions, networks, small world, heterogeneous beliefs, price dynamics, bifurcations, chaos

Properties of equilibrium asset prices under alternative learning schemes

This paper characterizes equilibrium asset prices under adaptive, rational and Bayesian learning schemes in a model where dividends evolve on a binomial lattice. The properties of equilibrium stock and bond prices under learning are shown to differ significantly compared with prices under full information rational expectations. Learning causes the discount factor and risk-neutral probability measure to become path-dependent and introduces serial correlation and volatility clustering in stock returns. We also derive conditions under which the expected value and volatility of stock prices will be higher under learning than under full information. Finally, we derive restrictions on prior beliefs under which Bayesian and rational learning lead to identical prices and show how the results can be generalized to more complex settings where dividends follow either multi-state i.i.d. distributions or multi-state Markov chains.Assets (Accounting) ; Rational expectations (Economic theory)

Optimal tree methods

Includes bibliographical references.Although traditional tree methods are the simplest numerical methods for option pricing, much work remains to be done regarding their optimal parameterization and construction. This work examines the parameterization of traditional tree methods as well as the techniques commonly used to accelerate their convergence. The performance of selected, accelerated binomial and trinomial trees is then compared to an advanced tree method, Figlewski and Gao's Adaptive Mesh Model, when pricing an American put and a Down-And-Out barrier option

Microscopic models of financial markets

This review deals with several microscopic models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation approaches in financial economics, we first give a summary of the Donangelo-Sneppen model of monetary exchange and compare it with related models in economics literature. Our selective review then outlines the main ingredients of some influential early models of multi-agent dynamics in financial markets (Kim-Markowitz, Levy-Levy-Solomon). As will be seen, these contributions draw their inspiration from the complex appearance of investors' interactions in real-life markets. Their main aim is to reproduce (and, thereby, provide possible explanations) for the spectacular bubbles and crashes seen in certain historical episodes, but they lack (like almost all the work before 1998 or so) a perspective in terms of the universal statistical features of financial time series. In fact, awareness of a set of such regularities (power-law tails of the distribution of returns, temporal scaling of volatility) only gradually appeared over the nineties. With the more precise description of the formerly relatively vague characteristics (e.g. moving from the notion of fat tails to the more concrete one of a power-law with index around three), it became clear that financial markets dynamics give rise to some kind of universal scaling laws. Showing similarities with scaling laws for other systems with many interacting subunits, an exploration of financial markets as multi-agent systems appeared to be a natural consequence. This topic was pursued by quite a number of contributions appearing in both the physics and economics literature since the late nineties. From the wealth of different flavors of multi-agent models that have appeared by now, we discuss the Cont-Bouchaud, Solomon-Levy-Huang and Lux-Marchesi models. Open research questions are discussed in our concluding section. --

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

On the Pricing of Forward Starting Options under Stochastic Volatility

We consider the problem of pricing European forward starting options in the presence of stochastic ­volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution based on Heston’s model of stochastic volatility