Model-free Analysis of Dynamic Trading Strategies

TL;DR

This paper presents a model-free, pathwise framework for analyzing dynamic trading strategies, focusing on excursions of trading signals, and introduces a novel decomposition method for scenario analysis without probabilistic assumptions.

Contribution

It introduces a new pathwise decomposition of trading signals into { extdelta}-excursions, enabling model-free analysis of trading strategies and a non-parametric simulation method.

Findings

Decomposition into { extdelta}-excursions is unique for continuous paths.

Expressions for trades, profit, and risk metrics are derived from excursions.

High-frequency limit relates to local time of the signal.

Abstract

We introduce a model-free approach for analyzing the risk and return for a broad class of dynamic trading strategies, including pairs trading, mean-reversion trading and other statistical arbitrage strategies, in terms of excursions of a trading signal away from a reference level. Our results are derived in a pathwise setting, without any probabilistic assumptions. We introduce the notion of {\delta}-excursion, defined as a path which deviates by {\delta} from a reference level before returning to this level. We show that every continuous path has a unique decomposition into {\delta}-excursions. This decomposition is useful for the scenario analysis of dynamic trading strategies, leading to simple expressions for the number of trades, realized profit, maximum loss, and drawdown. We show that the high-frequency limit of mean-reversion strategies may be described in terms of the (p-th order) local time of the signal. In particular, our results yield a financial interpretation of the local time of an irregular path. Finally, we describe a non-parametric scenario simulation method for generating paths whose excursion properties match those observed in empirical data.