论文标题
使用牛顿 - 拉夫森方法自动分化以通过二项式模型来求解库存期权的隐含波动率
Using the Newton-Raphson Method with Automatic Differentiation to Numerically Solve Implied Volatility of Stock Option through Binomial Model
论文作者
论文摘要
在Klibanov等人撰写的论文中，它提出了一种新的方法来计算欧洲股票期权的隐含波动，以解决黑色 - choles方程的不良反问题的解决方案。此外，它提出了一种基于该期权隐含波动性与基础股票波动性之间的差异的交易策略。除了黑色choles方程外，二项式模型是另一种用于欧洲选择的方法。而且，也可以通过此模型来计算隐含的波动率。在本文中，我们将Newton-Raphson方法和自动差异一起应用于数值近似于该模型的任意库存期权的隐含波动性。我们使用来自几何布朗尼运动模型和二项式模型本身的刺激数据以及2018年至2021年美国市场数据的数据提供了数学模型和方法，方法和测试结果的解释。
In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading strategy based on the difference between implied volatility of the option and the volatility of the underlying stock. In addition to the Black-Scholes equation, Binomial model is another method used to price European options. And, the implied volatility can be also calculated through this model. In this paper, we apply the Newton-Raphson method together with Automatic Differention to numerically approximate the implied volatility of an arbitrary stock option through this model. We provide an explanation of the mathematical model and methods, the methodology, and the results from our test using the stimulated data from the Geometric Brownian Motion Model and the Binomial Model itself, and the data from the US market data from 2018 to 2021.
