Insider Trading in
Continuous Time
Kerry Back
Washington University in St. Louis
The continuous-time version of Kyle’s (1985) model
of asset pricing with asymmetric information is
studied It is shown that there is a unique equilib-
rium pricing rule within a certain class. This pric-
ing rule is obtained in closed form for general
distributions of the asset value. A particular exam-
ple is a lognormal distribution, for which the equi-
librium price process is a geometric Brownian
motion. General trading strategies are allowed. In
equilibrium, the informed agent, who is risk neu-
tral has many optima, but be does not correlate
his trades locally with the noise trades nor does
be submit discrete orders.
In the Kyle (1985) model of asset pricing with asym-
metric information, traders submit order quantities to
risk-neutral market makers, who set peti-
tively and buy or sell for their own accounts to clear
the market. Excluding market makers, traders are of
two types: informed or noise traders. There is a single
risk-neutral informed trader, who rationally antici-
pates the effect of his orders on the price. The pres-
ence of noise traders makes it impossible for the unin-
formed to exactly invert the price and infer the
informed trader’s signal. Thus, markets are semi-
I am grateful to Fischer Black, David P. Brown, Eric Hughson, Pete Kyle,
Chris Lamoureux, Hal Pedersen, Avanidhar Subrahmanyam, Jaeyoung Sung,
and especially Phil Dybvig for ments and discussion. I also thank
the editor, Chester Spatt, and an anonymous referee ments that led
to improvements in the exposition. I am grateful for research support from
Batterymarch Financial Management. The article was originally entitled,
“Continuous Insider Trading and the Distribution of Asset Prices.” Address
correspondence to Kerry Back, Olin School of Business, Washington Uni-
versity in St. Louis, St. Louis, MO 63130.
The Review of Financial Studies 1992 Volume 5, number 3, pp.
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