2011
DOI: 10.2139/ssrn.1871969
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Optimal High Frequency Trading with Limit and Market Orders

Abstract: We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for getting the execution order priority, which is a crucial issue in h… Show more

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Cited by 78 publications
(107 citation statements)
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“…For example, there are algorithms that are designed to find the best execution prices for investors who wish to minimize the price impact of large buy or sell orders, e.g., Bertsimas and Lo (1998), Almgren (2003), Kharroubi and Pham (2010), and Bayraktar and Ludkovski (2012). Moreover, there are HF strategies that specialize in arbitraging across different trading venues, and that seek to profit from market making and from short-term deviations in stock prices, e.g., Cartea and Jaimungal (2013), Guilbaud and Pham (2013), Cartea, Jaimungal and Ricci (2014), and Guéant, Lehalle and Fernandez Tapia (2011).…”
Section: Introductionmentioning
confidence: 99%
“…For example, there are algorithms that are designed to find the best execution prices for investors who wish to minimize the price impact of large buy or sell orders, e.g., Bertsimas and Lo (1998), Almgren (2003), Kharroubi and Pham (2010), and Bayraktar and Ludkovski (2012). Moreover, there are HF strategies that specialize in arbitraging across different trading venues, and that seek to profit from market making and from short-term deviations in stock prices, e.g., Cartea and Jaimungal (2013), Guilbaud and Pham (2013), Cartea, Jaimungal and Ricci (2014), and Guéant, Lehalle and Fernandez Tapia (2011).…”
Section: Introductionmentioning
confidence: 99%
“…A pretty recent literature investigates optimal trading strategies with limit orders or with the combined use of market and limit orders [1,5,12,13,15,18,19] and option market making [7,26] , but to our knowledge, a hedging problem with limit orders has not been studied so far. Although the above-cited models adopt several simplifying assumptions, they result in stochastic control problems, which are rarely analytically tractable.…”
Section: Introductionmentioning
confidence: 99%
“…These traders arrive randomly, choose whether they want to execute immediately, determine how large their order sizes should be, and even cancel their orders at any time to exit the market strategically. Despite its complexity, models of order book dynamics are of great interest not only because they can be applied to optimize trade execution strategies (Alfonsi et al, 2010;Obizhaeva and Wang, 2006;Predoiu et al, 2011;Guilbaud and Pham, 2013;Goettler et al, 2005Goettler et al, , 2009), but also because these models provide insight into the relationship between supply and demand (Farmer et al, 2004;Foucault et al, 2005). Empirical studies indicate that the formation of short-term price behavior depends on the evolution of limit order books (Parlour, 1998;Harris and Panchapagesan, 2005;Rosu, 2009).…”
Section: Introductionmentioning
confidence: 99%