英文标题：
《Full and fast calibration of the Heston stochastic volatility model》
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作者：
Yiran Cui, Sebastian del Ba\\~no Rollin, Guido Germano
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最新提交年份：
2016
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英文摘要：
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston characteristic function and modify it to avoid discontinuities caused by branch switchings of complex functions. Using this representation, we obtain the analytical gradient of the price of a vanilla option with respect to the model parameters, which is the key element of all variants of the objective function. The interdependency between the components of the gradient enables an efficient implementation which is around ten times faster than a numerical gradient. We choose the Levenberg-Marquardt method to calibrate the model and do not observe multiple local minima reported in previous research. Two-dimensional sections show that the objective function is shaped as a narrow valley with a flat bottom. Our method is the fastest calibration of the Heston model developed so far and meets the speed requirement of practical trading.
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中文摘要：
本文提出了一种对赫斯顿随机波动率模型进行完整而有效校准的算法。我们将校准表示为一个非线性最小二乘问题。我们开发了赫斯顿特征函数的一种合适的表示形式，并对其进行了修改，以避免复杂函数的分支切换造成的不连续性。利用这种表示，我们得到了普通期权价格相对于模型参数的解析梯度，这是目标函数所有变量的关键元素。梯度各组成部分之间的相互依赖性使高效实现成为可能，其速度大约是数值梯度的十倍。我们选择Levenberg-Marquardt方法来校准模型，并且没有观察到之前研究中报道的多个局部极小值。二维剖面图显示，目标函数的形状是一个平底窄谷。我们的方法是迄今为止开发的赫斯顿模型的最快校准，满足实际交易的速度要求。
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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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