Dynamic Spread Trading

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 mean-reverting Ornstein-Uhlenbeck (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 risk-free 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.

[1]  T. Björk.  Arbitrage Theory in Continuous Time , 2019 .

[2]  Michael Boguslavsky,et al.  Arbitrage under Power , 2004 .

[3]  S. Johansen.  Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models , 1991 .

[4]  A. R. Norman,et al.  Portfolio Selection with Transaction Costs , 1990, Math. Oper. Res..

[5]  D. Hendry,et al.  Co-Integration and Error Correction : Representation , Estimation , and Testing , 2007 .

[6]  Andrew W. Lo,et al.  What Happened To The Quants In August 2007?: Evidence from Factors and Transactions Data , 2008 .

[7]  Erik Stafford,et al.  Limited Arbitrage in Equity Markets , 2000 .

[8]  C. Kenney,et al.  Numerical integration of the differential matrix Riccati equation , 1985 .

[9]  G. Vidyamurthy.  Pairs Trading: Quantitative Methods and Analysis , 2004 .

[10]  Mark Whistler,et al.  Trading Pairs: Capturing Profits and Hedging Risk with Statistical Arbitrage Strategies , 2004 .

[11]  Luis M. Viceira,et al.  Strategic Asset Allocation in a Continuous-Time VAR Model , 2002 .

[12]  R. Mazo.  On the theory of brownian motion , 1973 .

[13]  Arnold Neumaier,et al.  Estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[14]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[15]  G. Martín-Herrán.  Symplectic Methods for the Solution to Riccati Matrix Equations Related to Macroeconomic Models , 1999 .

[16]  A. Bergstrom.  CONTINUOUS TIME STOCHASTIC MODELS AND ISSUES OF AGGREGATION OVER TIME , 1984 .

[17]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[18]  Arnold Neumaier,et al.  Algorithm 808: ARfit—a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[19]  W. P. Malcolm,et al.  Pairs trading , 2005 .

[20]  P. Bossaerts.  Common nonstationary components of asset prices , 1988 .

[21]  Hong Liu,et al.  Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets , 2004 .

[22]  S. Mudchanatongsuk,et al.  Optimal pairs trading: A stochastic control approach , 2008, 2008 American Control Conference.

[23]  Ts Kim,et al.  Dynamic Nonmyopic Portfolio Behavior , 1994 .

[24]  Jakub W. Jurek,et al.  Dynamic Portfolio Selection in Arbitrage , 2007 .

[25]  Mark D. Schroder,et al.  Optimal Consumption and Portfolio Selection with Stochastic Differential Utility , 1999 .

[26]  Florian Herzog,et al.  Continuous-Time Multivariate Strategic Asset Allocation , 2004 .

[27]  Wei Xiong,et al.  Convergence trading with wealth effects: an amplification mechanism in financial markets , 2001 .

[28]  William N. Goetzmann,et al.  Pairs Trading: Performance of a Relative Value Arbitrage Rule , 2006 .