Trading and Market Microstructure
A dynamic herding model with interactions of trading volumes is introduced. At time $t$, an agent trades with a probability, which depends on the ratio of the total trading volume at time $t-1$ to its own trading volume at its last trade.…
We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask…
We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the development of financial instruments, with a dynamical picture of an interacting market, in a simple setting. The proliferation of financial instruments apparently…
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets…
We define a methodology to quantify market activity on a 24 hour basis by defining a scale, the so-called scale of market quakes (SMQ). The SMQ is designed within a framework where we analyse the dynamics of excess price moves from one…
We present a dynamical model for the price evolution of financial assets. The model is based in a two level structure. In the first stage one finds an agent-based model that describes the present state of the investors' beliefs,…
In this article, we develop a model for the evolution of real estate prices. A wide range of inputs, including stochastic interest rates and changing demands for the asset, are considered. Maximizing their expected utility, home owners make…
Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free…
A minimal model of a market of myopic non-cooperative agents who trade bilaterally with random bids reproduces qualitative features of short-term electric power markets, such as those in California and New England. Each agent knows its own…
We propose a simple model for the behaviour of longterm investors on a stock market, consisting of three particles, which represent the current price of the stock and the opinion of the buyers, respectively sellers, about the right trading…
This paper considers ideal gas-like models of trading markets, where each agent is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally, these models introduce different…
The algorithmic trading comes from digitalisation of the processing of trading assets on financial markets. Since 1980 the computerization of the stock market offers real time processing of financial information. This technological…
We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance,…
Recently, several new pari-mutuel mechanisms have been introduced to organize markets for contingent claims. Hanson introduced a market maker derived from the logarithmic scoring rule, and later Chen and Pennock developed a cost function…
In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset…
We introduce a fully probabilistic framework of consumer product choice based on quality assessment. It allows us to capture many aspects of marketing such as partial information asymmetry, quality differentiation, and product placement in…
In market modeling, one often treats buyers as a homogeneous group. In this paper we consider buyers with heterogeneous preferences and products available in many variants. Such a framework allows us to successfully model various market…
In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact…
The intraday pattern, long memory, and multifractal nature of the intertrade durations, which are defined as the waiting times between two consecutive transactions, are investigated based upon the limit order book data and order flows of 23…
We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information…