Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.

[1]  Robert M. Dammon,et al.  The Optimal Trading and Pricing of Securities with Asymmetric Capital Gains Taxes and Transaction Costs , 1996 .

[2]  E. Fama,et al.  Permanent and Temporary Components of Stock Prices , 1988, Journal of Political Economy.

[3]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[4]  G. Yin,et al.  LIQUIDATION OF A LARGE BLOCK OF STOCK WITH REGIME SWITCHING , 2008 .

[5]  G. Yin,et al.  Liquidation of a large block of stock , 2007 .

[6]  Q. Zhang,et al.  Stock Trading: An Optimal Selling Rule , 2001, SIAM J. Control. Optim..

[7]  Qing Zhang,et al.  Optimal stock liquidation in a regime switching model with finite time horizon , 2006 .

[8]  R. Huisman,et al.  Option Formulas for Mean-Reverting Power Prices with Spikes , 2002 .

[9]  R. H. Liu,et al.  Recursive Algorithms for Stock Liquidation: A Stochastic Optimization Approach , 2002, SIAM J. Optim..

[10]  Abel Cadenillas,et al.  Optimal trading of a security when there are taxes and transaction costs , 1999, Finance Stochastics.

[11]  George M. Constantinides,et al.  Capital Market Equilibrium with Personal Tax , 1983 .

[12]  Xin Guo,et al.  Optimal selling rules in a regime switching model , 2005, IEEE Transactions on Automatic Control.

[13]  R. H. Liu,et al.  Optimal Selling Rules in a Regime-Switching Exponential Gaussian Diffusion Model , 2008, SIAM J. Appl. Math..

[14]  A. Cowles,et al.  Some A Posteriori Probabilities in Stock Market Action , 1937 .

[15]  Timothy C. Johnson.  THE OPTIMAL TIMING OF INVESTMENT DECISIONS , 2006 .

[16]  Qing Zhang,et al.  Option pricing in a regime-switching model using the fast Fourier transform , 2006 .

[17]  Christian M. Hafner,et al.  Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis , 2001 .

[18]  Mihail Zervos,et al.  A Model for Reversible Investment Capacity Expansion , 2007, SIAM J. Control. Optim..

[19]  L. Bos,et al.  On a semi-spectral method for pricing an option on a mean-reverting asset , 2002 .

[20]  Mark P. Taylor,et al.  Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks , 2002 .