英文标题：
《Deep Learning-Based BSDE Solver for Libor Market Model with Application
  to Bermudan Swaption Pricing and Hedging》
---
作者：
Haojie Wang, Han Chen, Agus Sudjianto, Richard Liu, Qi Shen
---
最新提交年份：
2018
---
英文摘要：
  The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE grid approach is not particularly feasible due to Curse of Dimensionality. The standard Monte Carlo method for American/Bermudan swaption pricing more or less uses regression to estimate expected value as a linear combination of basis functions (Longstaff and Schwartz). However, Monte Carlo method only provides the lower bound for American option price. Another complexity is the computation of the sensitivities of the option, the so-called Greeks, which are fundamental for a trader\'s hedging activity. Recently, an alternative numerical method based on deep learning and backward stochastic differential equations appeared in quite a few researches. For European style options the feedforward deep neural networks (DNN) show not only feasibility but also efficiency to obtain both prices and numerical Greeks. In this paper, a new backward DNN solver is proposed for Bermudan swaptions. Our approach is representing financial pricing problems in the form of high dimensional stochastic optimal control problems, FBSDEs, or equivalent PDEs. We demonstrate that using backward DNN the high-dimension Bermudan swaption pricing and hedging can be solved effectively and efficiently. A comparison between Monte Carlo simulation and the new method for pricing vanilla interest rate options manifests the superior performance of the new method. We then use this method to calculate prices and Greeks of Bermudan swaptions as a prelude for other Libor callable derivatives.
---
中文摘要：
伦敦银行同业拆借利率市场模型是衍生品定价的主要利率期限结构模型，尤其是百慕大掉期期权和其他外来的伦敦银行同业拆借利率可赎回衍生品。对于数值实施，采用伦敦银行同业拆借利率市场模型的衍生品定价主要通过蒙特卡罗模拟进行。由于维数灾难，PDE网格方法不是特别可行。美国/百慕大互换期权定价的标准蒙特卡罗方法或多或少地使用回归来估计期望值，作为基函数的线性组合（Longstaff和Schwartz）。然而，蒙特卡罗方法只能提供美式期权价格的下限。另一个复杂性是期权敏感性的计算，即所谓的希腊期权，这是交易员对冲活动的基础。近年来，在许多研究中出现了一种基于深度学习和倒向随机微分方程的数值方法。对于欧式期权，前馈深度神经网络（DNN）不仅具有可行性，而且能够有效地获得价格和数值。本文针对百慕大Swaption提出了一种新的反向DNN求解器。我们的方法是将金融定价问题表示为高维随机最优控制问题、FBSDE或等效的PDE。我们证明了使用反向DNN可以有效地解决高维百慕大掉期期权定价和套期保值问题。蒙特卡罗模拟与普通利率期权定价新方法的比较表明，新方法具有优越的性能。然后，我们使用此方法计算百慕大掉期期权的价格和希腊价格，作为其他伦敦银行同业拆借利率可赎回衍生品的前奏。
---
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
--
一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
--

---
PDF下载：
-->