Convex Regularization Of Local Volatility Estimation
Convex Regularization Of Local Volatility Estimation
复制标题
局部波动率估计的凸正则化
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
J. Zubelli
中科院分区：
文献类型：
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作者：
V. Albani;A. Cezaro;J. Zubelli
我们采用凸正则化技术的问题，校准Dupire的局部波动率表面模型考虑到离散网格和噪声数据的实际要求。这种要求是买卖价差、报价量化以及远离价内水平的期权价格缺乏流动性的结果。我们得到的收敛速度和结果相比，在理想化的连续设置。我们的研究结果使我们能够分别考虑到由于价格噪声和那些由于离散化误差的不确定性，因此，允许估计更好的离散化水平，无论是在域中，并在图像中的参数解决方案运营商的Morozov的差异原则。我们用模拟和真实的市场数据来说明结果。我们还通过比较市场数据的隐含波动率价格与校准模型的计算价格来验证结果。
We apply convex regularization techniques to the problem of calibrating Dupire’s local volatility surface model taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far away from the at-the-money level. We obtain convergence rates and results comparable to those obtained in the idealized continuous setting. Our results allow us to take into account separately the uncertainties due to the price noise and those due to discretization errors, thus, allowing estimating better discretization levels both in the domain and in the image of the parameter to solution operator by a Morozov’s discrepancy principle. We illustrate the results with simulated as well as real market data. We also validate the results by comparing the implied volatility prices of market data with the computed prices of the calibrated model.
Banach 空间中 Tikhonov 正则化的序贯差异原理的正则化性质
影响因子：
1.1
作者：
S. W. Anzengruber;B. Hofmann;P. Mathé
通讯作者：
P. Mathé