Abstract
A model of insider trading in continuous time in which a risk-neutral insider possesses long-lived imperfect information on a risk asset is studied. By conditional expectation theory and filtering theory, we turn it into a model with insider knowing complete information about the asset with a revised risky value and deduce its linear Bayesian equilibrium consisting of optimal insider trading strategy and semistrong pricing rule. It shows that, in the equilibrium, as the degree of insider observing the signal of the risky asset value is more and more accurate, market depth, trading intensity, and residual information are all decreasing and the total expectation profit of the insider is increasing and that the information about the asset value incorporated into the equilibrium price, which has nothing to do with the volatility of noise trades, is increasing as time goes by, but not all information of asset value is incorporated into the price in the final disclosed time due to the incompleteness of insider’s observation, though the market depth is still a time-independent constant. Some simulations are illustrated to show these features. However, it is an open question of how to make maximal profit if the insider is risk-averse.
Highlights
Kyle [1] first proposed a mathematical continuous auction model of insider trading and proved that as time interval goes to zero, the equilibrium of sequential trading consisting of optimal insider trading strategies and semistrong pricing rules converges to a continuous-time version in which the market depth is a time-independent constant and all private information about the asset value is incorporated into the market price
Our main result is that it is the first time to study continuous-time insider trading with an Complexity insider knowing incomplete privation information on the risky asset and find that the more information the insider possesses, the more advantage the insider will take, but the information about the asset value cannot be incorporated into the market price all in the final disclosed time since the information about the asset value is not perfectly observed by the insider, while market depth, trading intensity, and residual information are all decreasing. ese results are in accord with our economic intuition, which are similar to those in discrete-time insider trading [17,18,19]
2 ε of the observing noise in risky asset value decreases, that is to say, the degree of insider observing the signal of the risky asset value is more and more accurate, market depth 1/λ (Figure 2(a)), trading intensity βt, and residual information Σt are all decreasing (Figures 2(b) and 2(c)), while the total expectation profit E(P) of the insider is increasing (Figure 2(d)). ese results can be understood since the more accurate the information held by the insider, the deeper the market depth is such that the insider makes more profit
Summary
Kyle [1] first proposed a mathematical continuous auction model of insider trading and proved that as time interval goes to zero, the equilibrium of sequential trading consisting of optimal insider trading strategies and semistrong pricing rules converges to a continuous-time version in which the market depth is a time-independent constant and all private information about the asset value is incorporated into the market price. Zhou [6] obtained a unique linear equilibrium of continuoustime insider trading with market makers observing some partial information on a risky asset. We will study a model of continuous-time insider trading, in which a risk-neutral insider possesses imperfect information on a static risk asset traded continuously in a time interval, and investigate the impact of the accurate degree of information observed by the insider on the market equilibrium.
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