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.
151 Estrategias de Trading (151 Trading Strategies)
这本书，这是在西班牙语，提供了详细的描述，包括超过550个数学公式，超过150个交易策略跨主机的资产类别（和交易风格）。这包括股票、期权、固定收益、期货、ETF、指数、大宗商品、外汇、可转换债券、结构性资产、波动性（作为一种资产类别）、不动产、不良资产、现金、加密货币、杂项（如天气、能源、通胀）、全球宏观、基础设施和税收套利。一些策略是基于机器学习算法（如人工神经网络，贝叶斯，k近邻）。我们还提供：用于说明样本外回溯测试的源代码和解释性注释;大约2，000个参考书目;以及900多个词汇表、缩略词和数学定义。本报告旨在提供描述性和教育性。- Este libro proporciones detalladas，que incluyen más de 550 fórmulas matemáticas，para más de 150 estrategias de trading para una acquisition de clases de activos y estilos de trading. Esto incluye acciones，opciones，bonos（renta fija），futuros，ETF，indices，commodities，divisas，bonos convertibles，activos estructurados，volatilidad（co…
Kernel Learning for Mean-Variance Trading Strategies
Imperial College London, Department of Mathematics（伦敦帝国理工学院数学系）；University of Oxford, Mathematical Institute and Oxford Man Institute（牛津大学数学研究所和牛津曼研究所）
