Pathwise Excursion Analysis for Dynamic Trading Strategies

Summary

This document introduces a model-free, pathwise method for analyzing the risk and return of dynamic strategies such as pairs trading, mean-reversion, and statistical arbitrage. It decomposes a continuous trading signal into δ-excursions: movements away from a reference level that return to that level. The method requires no probabilistic assumptions and uses the decomposition to derive scenario measures including trade counts, realized profit, maximum loss, and drawdown.

The document also connects the high-frequency limit of mean-reversion strategies to higher-order local time of the signal, giving local time a financial interpretation for irregular paths. It describes a non-parametric scenario simulation approach that generates paths with excursion characteristics matching empirical observations. The abstract does not specify the trading rules, calibration procedure, or validation results, so it outlines an analytical framework and simulation idea rather than a fully detailed implementation.

Key ideas

• Continuous signal paths can be uniquely decomposed into excursions of a chosen size away from a reference level.
• Excursion counts support scenario calculations for trades, realized profit, maximum loss, and drawdown.
• The framework analyzes strategy risk and return pathwise without probability assumptions.
• The high-frequency behavior of mean-reversion strategies is linked to local time of the signal.
• Non-parametric simulations can generate paths matching observed excursion properties.

Tags

# Model-free Analysis of Dynamic Trading Strategies


# Model-free Analysis of Dynamic Trading Strategies









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 δ-excursion, defined as a path which deviates by δ from a reference level before returning to this level. We show that every continuous path has a unique decomposition into δ-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.

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