Optimal convergence trading with unobservable pricing errors

We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (Rev Financ Stud 26(4):1048–1086, 2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation which is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain.

[1]  G. Teschl.  Ordinary Differential Equations and Dynamical Systems , 2012 .

[2]  A. Papanicolaou,et al.  Pairs Trading of Two Assets with Uncertainty in Co-Integration's Level of Mean Reversion , 2016 .

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

[4]  H. Kunita,et al.  Stochastic differential equations for the non linear filtering problem , 1972 .

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

[6]  Bahman Angoshtari.  On the Market-Neutrality of Optimal Pairs-Trading Strategies , 2016, 1608.08268.

[7]  R. Frey,et al.  EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies , 2017 .

[8]  Hoi Ying Wong,et al.  Mean-variance portfolio selection of cointegrated assets , 2011 .

[9]  S. Mitter,et al.  New results on the innovations problem for non-linear filtering , 1981 .

[10]  Yoichi Kuwana,et al.  CERTAINTY EQUIVALENCE AND LOGARITHMIC UTILITIES IN CONSUMPTION/INVESTMENT PROBLEMS , 1995 .

[11]  Jun Liu,et al.  Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities , 2000 .

[12]  U. Rieder,et al.  Portfolio optimization with unobservable Markov-modulated drift process , 2005, Journal of Applied Probability.

[13]  Marcos Escobar,et al.  PORTFOLIO OPTIMIZATION IN AFFINE MODELS WITH MARKOV SWITCHING , 2014, 1403.5247.

[14]  Sühan Altay,et al.  Pairs Trading Under Drift Uncertainty and Risk Penalization , 2017, International Journal of Theoretical and Applied Finance.

[15]  Abel Cadenillas,et al.  EXPLICIT SOLUTIONS OF CONSUMPTION‐INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING , 2009 .

[16]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[17]  Hans-Martin Krolzig,et al.  Statistical Analysis of Cointegrated VAR Processes with Markovian Regime Shifts , 1999 .

[18]  Sühan Altay,et al.  Pairs Trading under Drift Uncertainty and Risk Penalization , 2017 .

[19]  Jing Xu,et al.  Costly arbitrage through pairs trading , 2015 .

[20]  Jun Liu,et al.  Optimal Convergence Trade Strategies , 2013 .

[21]  Tomas Björk,et al.  Optimal investment under partial information , 2010, Math. Methods Oper. Res..

[22]  Abe de Jong,et al.  The Risk and Return of Arbitrage in Dual-Listed Companies , 2008 .

[23]  D. Crisan,et al.  Fundamentals of Stochastic Filtering , 2008 .

[24]  Nicole Bäuerle,et al.  Portfolio optimization with Markov-modulated stock prices and interest rates , 2004, IEEE Transactions on Automatic Control.

[25]  RÜDIGER FREY,et al.  PORTFOLIO OPTIMIZATION UNDER PARTIAL INFORMATION WITH EXPERT OPINIONS , 2012 .

[26]  Andrea Frazzini,et al.  Betting Against Beta , 2010 .

[27]  Algorithmic Trading of Co-Integrated Assets , 2015 .

[28]  W. Fleming,et al.  Optimal Control for Partially Observed Diffusions , 1982 .

[29]  Robert J. Elliott,et al.  New finite-dimensional filters and smoothers for noisily observed Markov chains , 1993, IEEE Trans. Inf. Theory.

[30]  Raphael Yan,et al.  Dynamic Pairs Trading Using the Stochastic Control Approach , 2012 .

[31]  B. Hansen,et al.  Testing for two-regime threshold cointegration in vector error-correction models , 2002 .

[32]  Robert J. Elliott,et al.  Estimating a regime switching pairs trading model , 2018 .

[33]  George Yin,et al.  Feynman-Kac formula for switching diffusions: connections of systems of partial differential equations and stochastic differential equations , 2013 .

[34]  Anand M. Vijh.  S&P 500 Trading Strategies and Stock Betas , 1994 .

[35]  Gang George Yin,et al.  Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model , 2003, SIAM J. Control. Optim..