Financial equilibrium with asymmetric information and random horizon (original) (raw)

Equilibria in financial markets with heterogeneous agents: a probabilistic perspective

Journal of Mathematical Economics, 2005

We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are "chartist" or extrapolatory rules. Prices can exhibit transient behaviour when chartists predominate. However, if the probability that an agent will switch to being a "chartist" is not too high then the process does not explode. There are occasional bubbles but they inevitably burst. In fact, we prove that the limit distribution of the price process exists and is unique. This limit distribution may be thought of as the appropriate equilibrium notion for such markets. A number of characteristics of financial time series can be captured by this sort of model. In particular, the presence of chartists fattens the tails of the stationary distribution.

Option Pricing in Markets with Informed Traders

International Journal of Theoretical and Applied Finance, 2020

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets, where we consider traders with information on the stock price direction and stock return mean. The Black–Scholes–Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

Incomplete and Asymmetric Information in Asset Pricing Theory

Lecture Notes in Mathematics, 2004

A considerable part of the vast development in Mathematical Finance over the last two decades was determined by the application of stochastic methods. These were therefore chosen as the focus of the 2003 School on "Stochastic Methods in Finance". The growing interest of the mathematical community in this field was also reflected by the extraordinarily high number of applications for the CIME-EMS School. It was attended by 115 scientists and researchers, selected from among over 200 applicants. The attendees came from all continents: 85 were Europeans, among them 35 Italians.

Financial markets with asymmetric information: An expository review of seminal models

International Review of Economics & Finance, 1998

The purpose of this paper is to make an expository review of the seminal models of the rational expectations equilibrium models in the finance literature. The staggering explosion of the complex research in this area of the finance literature has come to existence when the perfect market assumption of homogeneous information is relaxed and prices play the role of aggregating and transmitting information in the financial market. This expository review, therefore, brings out: (1) the seminal models (i.e., the models with a contribution to theory, rather than application of an existing theory); (2) the essential structure and theoretical contribution of each model in relation to the other models; and (3) the informational role of prices (i.e., fully-revealing versus partially-revealing nature of the models). This paper systematically brings out the seminal rational expectations equilibrium models in the following three categories. The first category being comprised of the pioneer models, Grossman (1976) and Grossman and Stiglitz (1980). The second category being composed of the price-taking competitive models, a direction initiated by Hellwig (1980). The third category including the non-price-taking non-competitive models, a direction initiated by Kyle (1984, 1985).

Kyle's Model with Stochastic Liquidity

arXiv (Cornell University), 2022

A. We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our equilibrium allows us to study the impact of the stochastic volatility of noise trading on the volatility of the asset. In particular, when the fundamental price is log-normally distributed, informed trading forces the log-return up to maturity to be Gaussian for any choice of noise-trading volatility even though the price process itself comes with stochastic volatility. Surprisingly, we nd that in equilibrium both Kyle's Lambda and its inverse (the market depth) are submartingales.

The Value of Information in Stochastic Control and Finance

Australian Economic Papers, 2005

We present an optimal portfolio problem with logarithmic utility in the following 3 cases: (i) The classical case, with complete information from the market available to the agent at all times. Mathematically this means that the portfolio process is adapted to the filtration F t of the underlying Brownian motion (or, more generally, the underlying Lévy process). (ii) The partial observation case, in which the trader has to base her portfolio choices on less information than F t. Mathematically this means that the portfolio process must be adapted to a filtration E t ⊆ F t for all t. For example, this is the case if the trader can only observe the asset prices and not the underlying Lévy process. (iii) The insider case, in which the trader has some inside information about the future of the market. This information could for example be the price of one of the assets at some future time. Mathematically this means that the portfolio process is allowed to be adapted to a filtration G t ⊇ F t for all t. In this case the associated stochastic integrals become anticipating, and it is necessary to explain what mathematical model it is appropriate to use and to clarify the corresponding anticipating stochastic calculus. We solve the problem in all these 3 cases and we compute the corresponding maximal expected logarithmic utility of the terminal wealth. Let us call these quantities V F , V E and V G , respectively. Then V F − V E represents the loss of value due the loss of information in (ii), and V G − V F is the value gained due to the inside information in (iii).

Asset Pricing under Asymmetric Information

2001

Asset prices are driven by public news and information that is dispersed among many market participants. Traditional asset pricing theories have assumed that all investors hold symmetric information. Research in the past two decades has shown that the inclusion of asymmetric information drastically alters traditional results. This book provides a detailed up‐to‐date survey that serves as a map for students and other researchers navigating through this literature. The book starts by introducing the reader to different knowledge, equilibrium, and efficiency concepts. After explaining no‐trade theorems, it highlights the important role of asymmetric information in explaining the existence and anatomy of bubbles. The subsequent overview of market microstructure models shows how information is reflected in prices and how traders can infer it from prices. Insights derived from herding models are used to provide explanations for stock market crashes. If investors have short horizons, price...

The no-arbitrage condition and financial markets with heterogeneous information

Journal of Economics and Finance, 1998

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, with M risky securities and S states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the noarbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.

Generalized Arrow Pricing to Understand Financial Markets

2020

Summary Most of the concepts that are used in modern theory of financial markets are contained in a paper published by Arrow in 1953. Arrow's model generalizes to non finite set of states describing uncertainty so as to encompass general financial assets pricing. We present several theorems of equivalence between General Equilibrium and Perfect Foresight Equilibrium (PFE), a concept adapted to financial assets markets. These results put forward several points: -The welfare properties of PFE, or in Arrow's term, the "role of securities in the optimal allocation of risk". -The role of the complete market hypothesis (CMS) and the reason why it takes an abstract mathematical form in modern finance. -The probabilistic interpretation of assets prices under the CMS hypothesis. This interpretation extends to dynamic models (as the equivalent martingale property) and allows the pricing of assets by their expected payments. -The necessary properties of equilibrium prices w...