Financial equilibrium with asymmetric information and random horizon

Umut Çetin ()
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Umut Çetin: London School of Economics and Political Science

Finance and Stochastics, 2018, vol. 22, issue 1, No 4, 97-126

Abstract: Abstract We study in detail and explicitly solve the version of Kyle’s model introduced in a specific case in Back and Baruch (Econometrica 72:433–465, 2004), where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensional diffusions. It turns out that such an equilibrium is only possible if the final payoff is Bernoulli distributed as in Back and Baruch (Econometrica 72:433–465, 2004). We show in the second part that the signal the market makers use in the general case is a time-changed version of the one they would have used had the final payoff had a Bernoulli distribution. In both cases, we characterise explicitly the equilibrium price process and the optimal strategy of the informed trader. In contrast to the original Kyle model, it is found that the reciprocal of the market’s depth, i.e., Kyle’s lambda, is a uniformly integrable supermartingale. While Kyle’s lambda is a potential, i.e., converges to 0, for the Bernoulli-distributed final payoff, its limit in general is different from 0.

Keywords: Kyle’s model; Financial equilibrium; One-dimensional diffusions; h $h$ -transform; Potential theory; 60J45; 60J60; 91B44 (search for similar items in EconPapers)
JEL-codes: D82 G12 G14 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s00780-017-0348-0

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