金融价格、期权和交易策略与似然理论的联系
文章 arXiv papers · 作者: Arnold Janssen et al.
总结
本文将无套利价格过程与统计实验中的滤波似然过程联系起来。文章说明如何通过统计检验来解释期权，并指出某些期权价格可以用检验效能表示。该框架将金融定价概念与勒卡姆发展出的似然理论方法联系起来。
作者概述了在某些情况下如何利用检验效能的变化推导Delta和Gamma交易策略，以及如何用统计推理离散地近似连续时间策略。文章还将伊藤型金融模型与基于风险函数的生存模型联系起来，并指出几何分数布朗运动的一个统计学对应形式。该文是对这些对应关系的概念性综述，没有提供实证表现结果，也不能证明推导出的策略在实践中能够盈利。
核心观点
- 无套利价格过程可以用滤波似然过程表示。
- 期权与统计检验相关联，某些价格与检验效能有关。
- 在特定情形下，检验效能动态可以支持推导Delta和Gamma策略。
- 可以使用统计论证离散地近似连续时间交易策略。
- 伊藤型模型和几何分数布朗运动在统计似然模型中都有对应形式。
标签
全文
# Statistical likelihood methods in finance # Statistical likelihood methods in finance It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and outlines some similarities between finance and the statistical likelihood theory of Le Cam. Options are linked to statistical tests of the underlying experiments. In particular, some price formulas for options are expressed by the power of related tests. In special cases the dynamics of power functions for filtered likelihood processes can be used to establish trading strategies which lead to formulas for the Greeks Delta and Gamma. Moreover statistical arguments are then used to establish a discrete approximation of continuous time trading strategies. It is explained that Ito type financial models correspond to hazard based survival models in statistics. Also price processes given by a geometric fractional Brownian motion have a statistical counterpart in terms of the likelihood theory of Gaussian statistical experiments.
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此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。