Strategic Insider Trading Equilibrium: A Filter Theory Approach (original) (raw)
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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.
Strategic Insider Trading Equilibrium: A Forward Integration Approach
SSRN Electronic Journal, 2007
The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing time-varying noise trading, and by allowing the orders of the noise traders to be correlated with the insider's signal. 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. 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.
A Risk-Averse Insider and Asset Pricing in Continuous Time
This paper derives an equilibrium asset price when there exist three kinds of traders in financial market: a risk-averse informed trader, noise traders, and risk neutral market makers. This paper is an extended version of Kyle's (1985, Econometrica) continuous time model by introducing insider's risk aversion. We obtain not only the equilibrium asset pricing and market depth parameter but also insider's value function and optimal insider's trading strategy explicitly. The comparative static shows that the market depth (the reciprocal of market pressure) increases with time and volatility of noise traders' trading.
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.
Finance and Stochastics, 2007
We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.
Insider trading equilibrium in a market with memory
Mathematics and Financial Economics, 2012
We consider the Kyle-Back model for insider trading, with the difference that the classical Brownian motion noise of the noise traders is replaced by the noise of a fractional Brownian motion B H with Hurst parameter H > 1 2 (when H = 1 2 , B H coincides with the classical Brownian motion). Heuristically, for H > 1 2 this means that the noise traders has some "memory", in the sense that any increment from time t on has a positive correlation with its value at t. (In other words, the noise trading is a persistent stochastic process). It also means that the paths of the noise trading process are more regular than in the classical Brownian motion case. We obtain an equation for the optimal (relative) trading intensity for the insider in this setting, and we show that when H → 1 2 the solution converges to the solution in the classical case. Finally, we discuss how the size of the Hurst coefficient H influences the optimal performance and portfolio of the insider.
Real and financial effects of insider trading with correlated signals
Economic Theory, 2000
In this paper we study the real and financial effects of insider trading in a Static, Kyle-type model. In our model the insider is also the manager of the firm. Hence the insider chooses both the amount of the real output to be produced and the amount of the stock of the firm to trade. The aim of the paper is to study the relationship between financial decisions and real decisions. In particular, we examine how insider trading on the stock market affects the real output and price and how the real decision making affects the financial variables, such as the extent of insider trading, stock prices, and the stock pricing rule of the market maker. In the model, the market maker observes two correlated signals: the total order flow and the market price of the real good. We study the informativeness of the stock price and the effects on insider's profits. We also construct a compensation scheme that aligns the interests of the insider and the firm. Finally, we generalize the pricing rule set up by a competitive market maker and analyze the comparative statics of the model.
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.
Insider trading with different market structures
International Review of Economics & Finance, 2012
We study an extension of with two insiders under three different market structures: (i) Cournot competition among the insiders, (ii) Stackelberg game between the insiders and (iii) Monopoly in the real market and Stackelberg in the financial market. We show how the equilibrium outcomes are affected by each of the market structure. Finally we perform a comparative statics analysis between the models. 1