英文标题：
《The Heston stochastic volatility model with piecewise constant
  parameters - efficient calibration and pricing of window barrier options》
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作者：
Daniel Guterding and Wolfram Boenkost
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最新提交年份：
2019
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英文摘要：
  The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with simple structure in time-direction. However, extending the model to the case of time-dependent parameters, which would allow for a parametrization of the market at multiple timepoints, proves more challenging. We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. We show that semi-analytical formulas can also be derived in this more complex case and combine them with recent advances in computational techniques for the Heston model. Our numerical scheme is based on the calculation of the characteristic function using Gauss-Kronrod quadrature with an additional control variate that stabilizes the numerical integrals. We use our method to calibrate the Heston model with piecewise constant parameters to the foreign exchange (FX) options market. Finally, we demonstrate improvements of the Heston model with piecewise constant parameters upon the standard Heston model in selected cases.
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中文摘要：
赫斯顿随机波动率模型是评估金融衍生品价值的标准模型，因为它可以使用半解析公式进行校准，并捕捉到时间方向结构简单的金融衍生品市场的最基本结构。然而，将模型扩展到与时间相关的参数的情况，这将允许在多个时间点对市场进行参数化，证明更具挑战性。我们提出了一种简单且数值有效的方法来校准具有分段常数参数的赫斯顿随机波动率模型。我们表明，在这种更复杂的情况下，也可以导出半解析公式，并将其与赫斯顿模型计算技术的最新进展相结合。我们的数值格式是基于使用高斯-克朗罗德求积和附加控制变量来计算特征函数，从而稳定数值积分。我们使用我们的方法对外汇期权市场的具有分段常数参数的赫斯顿模型进行了校准。最后，在选定的案例中，我们展示了具有分段常数参数的赫斯顿模型对标准赫斯顿模型的改进。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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