英文标题：
《A Probabilistic Approach to Nonparametric Local Volatility》
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作者：
Martin Tegn\\\'er and Stephen Roberts
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最新提交年份：
2019
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英文摘要：
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential component is a latent function which can be uniquely determined only in the limit of infinite data. To (re)construct this function, numerous calibration methods have been suggested involving steps of interpolation and extrapolation, most often of parametric form and with point-estimate representations. We look at the calibration problem in a probabilistic framework with a nonparametric approach based on a Gaussian process prior. This immediately gives a way of encoding prior beliefs about the local volatility function and a hypothesis model which is highly flexible yet not prone to over-fitting. Besides providing a method for calibrating a (range of) point-estimate(s), we draw posterior inference from the distribution over local volatility. This leads to a better understanding of uncertainty associated with the calibration in particular, and with the model in general. Further, we infer dynamical properties of local volatility by augmenting the hypothesis space with a time dimension. Ideally, this provides predictive distributions not only locally, but also for entire surfaces forward in time. We apply our approach to S&P 500 market data.
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中文摘要：
局部波动率模型是一种广泛用于金融衍生品定价和对冲的模型。虽然它的主要吸引力在于它能够再现观察到的期权价格的任何给定表面——它提供了一个完美的拟合——但其基本组成部分是一个潜在函数，只有在无限数据的限制下才能唯一确定。为了（重新）构建该函数，已经提出了许多校准方法，包括插值和外推步骤，最常见的是参数形式和点估计表示。我们在基于高斯过程先验的非参数方法的概率框架下研究校准问题。这立即提供了一种编码有关局部波动率函数的先验信念的方法，以及一种高度灵活但不容易过度拟合的假设模型。除了提供校准点估计（范围）的方法外，我们还从局部波动率的分布中得出后验推断。这有助于更好地理解与校准相关的不确定性，尤其是与模型相关的不确定性。此外，我们通过增加假设空间的时间维度来推断局部波动的动力学性质。理想情况下，这不仅可以提供局部预测分布，还可以提供整个曲面的预测分布。我们将我们的方法应用于标准普尔500指数的市场数据。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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