Related papers: A Classical Model of Speculative Asset Price Dynam…
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws…
Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time.…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…
We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market…
In speculative markets, risk-free profit opportunities are eliminated by traders exploiting them. Markets are therefore often described as "informationally efficient", rapidly removing predictable price changes, and leaving only residual…
A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change…
We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on an excess…
We present a dynamical theory of asset price bubbles that exhibits the appearance of bubbles and their subsequent crashes. We show that when speculative trends dominate over fundamental beliefs, bubbles form, leading to the growth of asset…
We describe a simple model for speculative trading based on adaptive behavior of economic agents.The adaptive behavior is expressed through a feedback mechanism for changing agents' stock-to-bond ratios, depending on the past performance of…
We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…