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Financial Markets and Trading: An Introduction to Market Microstructure and Trading Strategies by Anatoly B. Schmidt

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CHAPTER 5

Models of theLimit-Order Markets

Two former chapters were devoted to the models for dealer markets. With proliferation of order-driven continuous trading platforms, theoretical research has also focused on the markets where each trader can become a maker or a taker. The critical question for a trader in an order-driven market is whether to submit a market order for immediacy and for minimizing an opportunity cost,1 or to submit a limit order, which saves the spread but has uncertainty of execution. A compromise in this strategy is placing a limit order inside the market, which narrows the bid/ask spread and increases probability of execution. Ambiguity of this choice remains a challenge for both theoreticians and practitioners.2 In this chapter, several noted models of limit-order markets are described. I start with introducing one of the first contributions to analysis of this problem by Cohen, Maier, Schwartz, and Whitcomb (1981, called further CMSW). Then, I proceed with the models offered by Parlour (1998) and Foucault (1999). I conclude with an overview of recent developments in this field (see Parlour & Seppi 2008, for details).

THE CMSW MODEL

In the CMSW model, all traders are assumed to maximize their wealth, which consists of cash and a risky asset. Traders trade only at a set of fixed points of time. Trading costs include a fee for submitting a limit order and another fee paid in case an order is filled. It is assumed that trading is symmetric on both sides ...

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