Insider trading equilibrium in a market with memory (original) (raw)

A White Noise Approach to Insider Trading

Let Us Use White Noise, 2017

We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.

Strategic Insider Trading in Continuous Time: A New Approach

SSRN Electronic Journal, 2019

The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized by allowing time-varying noise trading. From rather simple assumptions we are able to derive the optimal trade for an insider; the trading intensity satisfies a deterministic integral equation, given perfect inside information, which we give a closed form solution to. We use a new technique called forward integration in order to find the optimal trading strategy. This is an extension of the stochastic integral which takes account of the informational asymmetry inherent in this problem. The market makers' price response is found by the use of filtering theory. The novelty is our approach, which could be extended in scope.

Converse trading strategies, intrinsic noise and the stylized facts of financial markets

Quantitative Finance, 2012

The paper proposes a simple asset pricing model with three groups of traders: chartists who believe in the persistence of bull and bear markets, fundamentalists who bet on a reduction of the observed mispricing, and investors who follow a buy and hold strategy. The innovative feature of the model concerns the frequency of trading: rather than remaining constant over time, each agent in a group is only assumed to become active with a certain probability over a given market period. Depending on the trading strategies, part of this elementary kind of intrinsic noise is additive and another part is multiplicative. Using bootstrap and Monte Carlo methods, it is demonstrated that this combination can contribute to explaining the stylized facts of the daily returns on financial markets, such as volatility clustering, fat tails, and the autocorrelation patterns. JEL classification: D84; G12; G14; G15.

Noise Trader Risk in Financial Markets

Journal of Political Economy, 1990

We present a simple overlapping generations model of an asset market in which irrational noise traders with erroneous stochastic beliefs both affect prices and earn higher expected returns. The unpredictability of noise traders' beliefs creates a risk in the price of the asset that deters rational arbitrageurs from aggressively betting against them. As a result, prices can diverge significantly from fundamental values even in the absence of fundamental risk. Moreover, bearing a disproportionate amount of risk that they themselves create enables noise traders to earn a higher expected return than do rational investors. The model sheds light on a number of financial anomalies, including the excess volatility of asset prices, the mean reversion of stock returns, the underpricing of closed end mutual funds, and the Mehra-Prescott equity premium puzzle.

Insider Trading With Stochastic Valuation

SSRN Electronic Journal, 2007

This paper studies a model of strategic trading with asymmetric information of an asset whose value follows a Brownian motion. An insider continuously observes a signal that tracks the evolution of the asset fundamental value. At a random time a public announcement reveals the current value of the asset to all the traders. The equilibrium has two regimes separated by an endogenously determined time T. In [0, T), the insider gradually transfers her information to the market and the market's uncertainty about the value of the asset decreases monotonically. By time T all her information is transferred to the market and the price agrees with the market value of the asset. In the interval [T, ∞), the insider trades large volumes and reveals her information immediately, so market prices track the market value perfectly. Despite this market efficiency, the insider is able to collect strictly positive rents after T. † We gratefully acknowledge the feedback of David Pearce. We also thanks Markus Brunnermeier, Lasse Pedersen, and Debraj Ray and seminar participants at NYU.

Monopolistic insider trading in a stationary market

This paper examines trading behavior of market participants and how quickly private information is revealed to the public. in a stationary financial market with asymmetric information. We establish reasonable assumptions, under which the market is not efficient in the strong form. in contrast to the Chau and Vayanos (2008) model. First, we assume that the insider bears a quadratic transaction cost. We find that the trading intensity of tilhe insider is inversely related to transaction cost and that the market maker's uncertainty about private signals is positively related to transaction cost. As transaction cost approaches zero, the economy converges to that of the Chau and Vayanos (2008) model. Second, we assume that the insider can observe signals only discretely and at evenly spaced times, at a lower frequency than that at which trading takes place. The sparseness of signals induces insiders to trade patiently before the next signal comes in, as in the finite horizon model of Kyle (1985). Furthermore, the degree of market efficiency declines as signals arrive more sparsely. Finally, we assume that arrival times of private insider signals are random. In such case, the insider is less patient and trades more smoothly than with fixed arrival times As a result. market prices incorporate private information more quickly.

Point process bridges and weak convergence of insider trading models

Electronic Journal of Probability, 2013

We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten-Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465, when the common intensity of the Poisson processes tends to infinity.