The Fundamental Theorem of Derivative Trading - exposition, extensions and experiments
The Fundamental Theorem of Derivative Trading - exposition, extensions and experiments
复制标题
衍生品交易基本定理 - 阐述、扩展和实验
DOI：
10.1080/14697688.2016.1222078
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发表时间：
2017
影响因子：
1.3
通讯作者：
R. Poulsen
中科院分区：
文献类型：
--
作者：
Simon Ellersgaard;Martin Jönsson;R. Poulsen
当估计的波动率与现实不完全一致时，Delta套期保值期权组合将随着时间的推移产生非零损益。然而，有一个令人惊讶的简单公式来计算由此产生的对冲误差，这是自20世纪90年代末以来就知道的。我们称之为衍生品交易的基本定理。本文是对这一结果的一个调查。我们证明了它的一个更一般的版本，并讨论了各种扩展和应用，从纳入一个多维的跳跃框架，推导出Dupire-Gyöngy-Derman-Kani公式。我们还考虑了它的实际后果，无论是在模拟实验和经验数据，从而证明了隐含波动率对冲的好处。
When estimated volatilities are not in perfect agreement with reality, delta-hedged option portfolios will incur a non-zero profit-and-loss over time. However, there is a surprisingly simple formula for the resulting hedge error, which has been known since the late 1990s. We call this The Fundamental Theorem of Derivative Trading. This paper is a survey with twists on that result. We prove a more general version of it and discuss various extensions and applications, from incorporating a multi-dimensional jump framework to deriving the Dupire–Gyöngy–Derman–Kani formula. We also consider its practical consequences, both in simulation experiments and on empirical data, thus demonstrating the benefits of hedging with implied volatility.