On Feedforward Stock Trading Control Using a New Transaction Level Price Trend Model

Abstract

In this article, we provide a new Markovian-type model for stock price trend analysis at the transaction level, and illustrate its use for trading in conjunction with a controller, which makes buy and sell decisions. Central to our formulation is a sequence of i.i.d. random variables <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_k$</tex-math></inline-formula> , which corresponds to the number of transactions between reversals in price direction. For a trader, this is an important indicator of the “duration” of a trend. For processes with “large” <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_k$</tex-math></inline-formula> , there is an incentive to try and capitalize by buying stock when a temporary trend is “up” and selling when it is “down.” The extent to which this is possible is determined by a model parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p_e$</tex-math></inline-formula> , called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probability of efficiency</i> , which indicates the likelihood that the bid, ask, and current price are such that one can seamlessly enter or exit the market without slippage. The degree to which a trader can exploit trending behavior is quantified in our main result, which provides the expected value of the trading gain resulting from a strategically constructed feedforward switching controller. This article also includes an example illustrating application of the theory using historical data.