英文标题：
《Local Volatility Calibration by Optimal Transport》
---
作者：
Ivan Guo, Gr\\\'egoire Loeper, Shiyi Wang
---
最新提交年份：
2018
---
英文摘要：
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire\'s formula [6], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that can only be obtained via some form of price interpolation. In this paper, we propose a new local volatility calibration technique using the theory of optimal transport. We formulate a time continuous martingale optimal transport problem, which seeks a martingale diffusion process that matches the known densities of an asset price at two different dates, while minimizing a chosen cost function. Inspired by the seminal work of Benamou and Brenier [1], we formulate the problem as a convex optimization problem, derive its dual formulation, and solve it numerically via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm. The solution effectively reconstructs the dynamic of the asset price between the two dates by recovering the optimal local volatility function, without requiring any time interpolation of the option prices.
---
中文摘要：
从可观测期权价格校准波动率模型是定量金融中的一个基本问题。行业从业者最常用的方法是基于著名的杜皮尔公式[6]，该公式要求了解连续的罢工和到期日的普通期权价格，而这些价格只能通过某种形式的价格插值获得。在本文中，我们利用最优传输理论提出了一种新的局部波动率校准技术。我们构造了一个时间连续的鞅最优运输问题，该问题寻求一个鞅扩散过程，该过程与两个不同日期的已知资产价格密度相匹配，同时最小化所选的成本函数。受Benamou和Brenier[1]开创性工作的启发，我们将该问题表述为一个凸优化问题，推导其对偶公式，并通过增广拉格朗日方法和交替方向乘子法（ADMM）算法对其进行数值求解。该解决方案通过恢复最优局部波动率函数，有效地重建了两个日期之间资产价格的动态，无需对期权价格进行任何时间插值。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->