Optimal Trading Algorithms under Regime Switching

Abstract

In this article, the author is concerned with the problem of efficiently trading a large position in the marketplace when the stock price dynamic follows a regime-switching process. If the execution of a large order is not done properly, this will certainly lead to large losses. Given that the execution of a large position may take several trading days, it is therefore reasonable to assume that the market microstructure may change during the execution of the order. To address this possibility, the author assumes that the stock price follows a regime-switching model. This article is particularly interested in trading algorithms that track market benchmarks such as the volume-weighted average price (VWAP) and the minimum execution shortfall. The author proposes trading algorithms that break the execution order into small pieces and execute them over a predetermined period of time so as to minimize the overall execution shortfall or exceed the overall market VWAP. The underlying problem is formulated as a discrete-time stochastic optimal control problem with resource constraints. The value function and optimal trading strategies are derived in closed form. Numerical simulations with market data are reported to illustrate the pertinence of the approach.