摘要翻译：
本文研究了随机波动利率曲线的单因素Heath-Jarrow-Morton模型。它的自然形式用随机微分方程描述，通过蒙特卡罗模拟求解，通常涉及相当大的计算时间，从实际（金融）角度来看效率低下。该模型在三维上是马尔可夫的，因此可以映射为一个三维偏微分方程问题。本文提出了一种求解三维偏微分方程模型的优化数值方法，该方法既具有较低的计算时间，又具有合理的精度，这是一个实用的基本准则。空间离散化和时间离散化分别采用有限差分格式和Crank-Nicholson格式，采用尺度分析和交替方向隐式格式大大提高了计算效率。对收敛准则和计算时间等几个数值问题进行了分析和讨论。
---
英文标题：
《Fast resolution of a single factor Heath-Jarrow-Morton model with
  stochastic volatility》
---
作者：
Eusebio Valero, Manuel Torrealba, Lucas Lacasa and Fran\c{c}ois
  Fraysse
---
最新提交年份：
2011
---
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
--

---
英文摘要：
  This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a practical (financial) perspective. This model turns to be Markovian in three dimensions and therefore it can be mapped into a 3D partial differential equations problem. We propose an optimized numerical method to solve the 3D PDE model in both low computation time and reasonable accuracy, a fundamental criterion for practical purposes. The spatial and temporal discretization are performed using finite-difference and Crank-Nicholson schemes respectively, and the computational efficiency is largely increased performing a scale analysis and using Alternating Direction Implicit schemes. Several numerical considerations such as convergence criteria or computation time are analyzed and discussed.
---
PDF链接：
https://arxiv.org/pdf/1108.1688