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连续时间交易策略的路径分析与对冲

文章 arXiv papers · 作者: Candia Riga
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总结

论文提出一个连续时间交易分析框架，无需使用随机积分或概率模型。该框架直接根据价格路径定义收益和自融资条件，同时力求在加入概率模型后与经典定义保持一致。该方法使用非前瞻函数演算，涵盖广泛的路径依赖策略，包括 delta 对冲，并分别适用于连续价格路径和 càdlàg 价格路径。

另一项结果给出了逐路径复制定理，拓展了扩散模型金融学中的相关结果；此外，还针对指定情形给出路径依赖衍生品进行 delta 对冲时的对冲误差显式公式。作者还为其关于价格路径的假设提供了经济学解释。所提供的描述没有详细说明假设，也没有提供实证验证，因此主要呈现的是一个数学框架及相关结果，而非实际交易表现的证据。

核心观点

  • 该框架直接依据价格路径分析连续时间交易，无需概率工具。
  • 该框架为广泛的路径依赖策略定义收益过程和自融资条件。
  • 研究涵盖 delta 对冲策略，并提供适用于连续和 càdlàg 价格路径的版本。
  • 逐路径复制结果给出了指定情形下的对冲误差公式。
  • 论文为其价格路径假设提供了经济学依据。

标签

衍生品定价期权风险管理统计学
全文
# A pathwise approach to continuous-time trading


# A pathwise approach to continuous-time trading









This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a pathwise self-financial condition for continuous-time trading strategies, which is consistent with the classical definition in case a probability model is introduced. Our first proposition provides us with a pathwise definition of the gain process for a large class of continuous-time, path-dependent, self-finacing trading strategies, including the important class of 'delta-hedging' strategies, and is based on the recently developed 'non-anticipative functional calculus'. Two versions of the statement involve respectively continuous and càdlàg price paths. The second proposition is a pathwise replication result that generalizes the ones obtained in the classical framework of diffusion models. Moreover, it gives an explicit and purely pathwise formula for the hedging error of delta-hedging strategies for path-dependent derivatives across a given set of scenarios. We also provide an economic justification of our main assumption on price paths.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。