A Confidence Interval Triggering Method for Stock Trading

A Confidence Interval Triggering Method for Stock Trading Via Feedback Control S. Iwarere and B. Ross Barmish Abstract— This paper builds upon the robust control paradigm for stock trading established in [1]. To this end, the contribution of the current work is an algorithm for triggering a trade. Whereas previous work considered the management of a trade, this paper concentrates on entry into the trade. That is, based on historical prices, we generate, three possible signals: long, short or no trade. These signals are derived using an Ito process model based on geometric Brownian motion. The parameters of this model, the Ito process drift and the volatility , are estimated and adaptively updated as each new piece of price data

arrives. The confidence interval for determines when a trade is triggered. If a trade is triggered, then the amount invested in stock is obtained using the saturation-reset linear feedback controller described in [1]. The performance of this trading method is studied in both idealized markets and real- world markets. I. INTRODUCTION This paper is part of a relatively new branch of technical analysis which involves the application of control theoretic concepts to stock and option trading. The key idea in this literature is to formulate the trading law as a feedback control on the price sequence. Subsequently, buy and sell signals are generated over time and the trader’s holdings correspondingly change; e.g., see [1] for the author’s approach and the earlier work in [2]-[5]. In the control theory literature to date, the “triggering mechanism” for entering or exiting a trade has not been emphasized. This issue is the main focal point of this paper. We begin by first considering the triggering issue in a so-called idealized market. To this end, an underlying Ito process with unknown drift parameter and volatility parameter is assumed for the discrete-time stock price process S(k). Then, given n price measurements, we proceed to create an estimate ^ of and use the corresponding confidence interval to decide whether to enter a trade or “walk away.” Then, if the lower confidence level L satisfies L 0, a long trade is triggered. On the other hand, if the upper confidence level U satisfies U 0, this dictates going short. Finally, for the case when L< 0
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