doi: 10.3934/naco.2022014
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Optimal pairs trading of mean-reverting processes over multiple assets

1. 

School of Mathematical Sciences, Nankai University, Tianjin, 300071, China

2. 

School of Finance, Nankai University, Tianjin, 300071, China

*Corresponding author: Lihua Bai

Received  November 2021 Revised  April 2022 Early access May 2022

This paper studies multi-asset pairs trading strategies of maximizing the expected exponential utility of terminal wealth. We model the log-relationship between each pair of stock prices as an Ornstein-Uhlenbeck (O-U) process, and formulate a portfolio optimization problem. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman (HJB) equation, we characterize the optimal strategies and provide a verification result for the value function. Finally, we give some numerical results to show the characteristics of pairs trading.

Citation: Pengxu Xie, Lihua Bai, Huayue Zhang. Optimal pairs trading of mean-reverting processes over multiple assets. Numerical Algebra, Control and Optimization, doi: 10.3934/naco.2022014
References:
[1]

B. Angoshtari and T. Leung, Optimal dynamic basis trading, Annals of Finance, 15 (2019), 307-335.  doi: 10.1007/s10436-019-00348-x.

[2]

F. E. Benth and K. H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stochastic Analysis and Applications, 23 (2005), 687-704.  doi: 10.1081/SAP-200064457.

[3]

B. Do, R. Faff and K. Hamza, A new approach to modeling and estimation for pairs trading, In Proceedings of 2006 Financial Man agement Association European Conference, Stockholm, June 2006.

[4]

R. J. ElliottJ. van der Hoek and W. P. Malcolm, Pairs trading, Quantitative Finance, 5 (2005), 271-276.  doi: 10.1080/14697680500149370.

[5]

E. GatevW. N. Goetzmann and K. G. Rouwenhorst, Pairs trading: performance of a relative value arbitrage rule, Social Science Electronic Publishing, 19 (2006), 797-827. 

[6]

J. W. Jurek and H. Yang, Dynamic Portfolio Selection in Arbitrage, SSRN Electronic Journal, 2007.

[7]

S. Mudchanatongsuk, J. A. Primbs and W. Wong, Optimal pairs trading: A stochastic control approach, American Control Conference IEEE, 2008.

[8]

A. Tourin and R. Yan, Dynamic pairs trading using the stochastic control approach, Journal of Economic Dynamics and Control, 37 (2013), 1972-1981.  doi: 10.1016/j.jedc.2013.05.010.

[9]

G. Vidyamurthy, Pairs Trading: Quantitative Methods and Analysis, John Wiley Sons, 2004.

show all references

References:
[1]

B. Angoshtari and T. Leung, Optimal dynamic basis trading, Annals of Finance, 15 (2019), 307-335.  doi: 10.1007/s10436-019-00348-x.

[2]

F. E. Benth and K. H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stochastic Analysis and Applications, 23 (2005), 687-704.  doi: 10.1081/SAP-200064457.

[3]

B. Do, R. Faff and K. Hamza, A new approach to modeling and estimation for pairs trading, In Proceedings of 2006 Financial Man agement Association European Conference, Stockholm, June 2006.

[4]

R. J. ElliottJ. van der Hoek and W. P. Malcolm, Pairs trading, Quantitative Finance, 5 (2005), 271-276.  doi: 10.1080/14697680500149370.

[5]

E. GatevW. N. Goetzmann and K. G. Rouwenhorst, Pairs trading: performance of a relative value arbitrage rule, Social Science Electronic Publishing, 19 (2006), 797-827. 

[6]

J. W. Jurek and H. Yang, Dynamic Portfolio Selection in Arbitrage, SSRN Electronic Journal, 2007.

[7]

S. Mudchanatongsuk, J. A. Primbs and W. Wong, Optimal pairs trading: A stochastic control approach, American Control Conference IEEE, 2008.

[8]

A. Tourin and R. Yan, Dynamic pairs trading using the stochastic control approach, Journal of Economic Dynamics and Control, 37 (2013), 1972-1981.  doi: 10.1016/j.jedc.2013.05.010.

[9]

G. Vidyamurthy, Pairs Trading: Quantitative Methods and Analysis, John Wiley Sons, 2004.

Figure 1.  The stock price for $ A^1 $, $ B^1 $, $ A^2 $ and $ B^2 $
Figure 2.  The optimal wealth process $ X^* $
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