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Market making and mean reversion
 In Proc. ACM Conf. on Elec. Commerce
, 2011
"... Market making refers broadly to trading strategies that seek to profit by providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of time series models for the evolution of a ..."
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Market making refers broadly to trading strategies that seek to profit by providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of time series models for the evolution of a stock’s price. We first provide a precise theoretical characterization of the profitability of a simple and natural market making algorithm in the absence of any stochastic assumptions on price evolution. This characterization exhibits a tradeoff between the positive effect of local price fluctuations and the negative effect of net price change. We then use this general characterization to prove that market making is generally profitable on mean reverting time series — time series with a tendency to revert to a longterm average. Mean reversion has been empirically observed in many markets, especially foreign exchange and commodities. We show that the slightest mean reversion yields positive expected profit, and also obtain stronger profit guarantees for a canonical stochastic mean reverting process, known as the OrnsteinUhlenbeck (OU) process, as well as other stochastic mean reverting series studied in the finance literature. We also show that market making remains profitable in expectation for the OU process even if some realistic restrictions on trading frequency are placed on the market maker.
Optimal liquidation of pairs trade
, 2009
"... Abstract. Pairs trading is a common strategy used by hedge funds. When the spread between two highly correlated assets is observed to deviate from historical observations, a long position is taken in the underpriced asset and a short position in the overpriced one. If the spread narrows, both posit ..."
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Abstract. Pairs trading is a common strategy used by hedge funds. When the spread between two highly correlated assets is observed to deviate from historical observations, a long position is taken in the underpriced asset and a short position in the overpriced one. If the spread narrows, both positions are closed, thus generating a profit. We study when to optimally liquidate a pairs trading strategy when the difference between the two assets is modeled by an OrnsteinUhlenbeck process. We also provide a sensitivity analysis in the model parameters. 1.
PROFITABILITY OF PAIRS TRADING STRATEGY IN FINLAND
, 2010
"... Work in process. Comments welcome. ..."
Bargaining and Pricing in Networked Economic Systems
, 2011
"... Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, w ..."
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Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, we model an economic system as a combination of many bilateral economic opportunities, such as that between a buyer and a seller. The transactions are complicated by the existence of many economic opportunities, and the influence they have on each other. For example, there may be several prospective sellers and buyers for the same item, with possibly differing costs and values. Such a system may be modeled by a network, where the nodes represent players and the edges represent opportunities. We study the effect of network structure on the outcome of bargaining among players, through theoretical
Statistical estimation of multivariate OrnsteinUhlenbeck processes and applications to cointegration
, 2010
"... OrnsteinUhlenbeck models are continuoustime processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate ..."
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OrnsteinUhlenbeck models are continuoustime processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate OrnsteinUhlenbeck model driven by a multivariate regularly varying Lévy process with infinite variance. We show that the estimator is consistent. Moreover, we derive its asymptotic behavior and test statistics. The results are compared to the finite variance case. For the proof we require some new results on multivariate regular variation of products of random vectors and central limit theorems. Furthermore, we embed this model in the setup of a cointegrated model in continuous time.
Dynamic Spread Trading
, 2008
"... This paper is concerned with a dynamic trading strategy, which involves multiple synthetic spreads each of which involves long positions in a basket of underlying securities and short positions in another basket. We assume that the spreads can be modeled as meanreverting OrnsteinUhlenbeck (OU) pro ..."
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This paper is concerned with a dynamic trading strategy, which involves multiple synthetic spreads each of which involves long positions in a basket of underlying securities and short positions in another basket. We assume that the spreads can be modeled as meanreverting OrnsteinUhlenbeck (OU) processes. The dynamic trading strategy is implemented as the solution to a stochastic optimal control problem that dynamically allocates capital over the spreads and a riskfree asset over a finite horizon to maximize a general constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA) utility function of the terminal wealth. We show that this stochastic control problem is computationally tractable. Specifically, we show that the coefficient functions defining the optimal feedback law are the solutions of a system of ordinary differential equations (ODEs) that are the essence of the tractability of the stochastic optimal control problem. We illustrate the dynamic trading strategy with four pairs that consist of seven S&P 500 index stocks, which shows that the performance achieved by the dynamic spread trading strategy is significant and robust to realistic transaction costs. Key words: convergence trading, dynamic trading, mean reversion, pairs trading, statistical arbitrage, stochastic optimal control. 1