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Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory. (English) Zbl 1471.91519

Summary: In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.

MSC:

91G10 Portfolio theory
91G30 Interest rates, asset pricing, etc. (stochastic models)
91G80 Financial applications of other theories
60G22 Fractional processes, including fractional Brownian motion
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