Mathematical Foundations of Realtime Equity Trading. Liquidity Deficit and Market Dynamics. Automated Trading Machines

TL;DR

This paper develops a mathematical framework based on liquidity deficit to explain market dynamics and proposes an automated trading system resilient to losses, with promising results close to breakeven after costs.

Contribution

It introduces a novel calculus-based approach to model liquidity deficit and formulates a dynamic equation for automated trading based on P&L dynamics.

Findings

Liquidity deficit drives market behavior

Proposed trading system is resilient to catastrophic losses

Results are promising but near breakeven after fees

Abstract

We postulates, and then show experimentally, that liquidity deficit is the driving force of the markets. In the first part of the paper a kinematic of liquidity deficit is developed. The calculus-like approach, which is based on Radon--Nikodym derivatives and their generalization, allows us to calculate important characteristics of observable market dynamics. In the second part of the paper this calculus is used in an attempt to build a dynamic equation in the form: future price tend to the value maximizing the number of shares traded per unit time. To build a practical automated trading machine P&L dynamics instead of price dynamics is considered. This allows a trading automate resilient to catastrophic P&L drains to be built. The results are very promising, yet when all the fees and trading commissions are taken into account, are close to breakeven. In the end of the paper important criteria for automated trading systems are presented. We list the system types that can and cannot make money on the market. These criteria can be successfully applied not only by automated trading machines, but also by a human trader.