The calibration problem of implied volatility surface under complex financial models can be formulated as a nonlinear high-dimensional optimization'/> Monte Carlo calibration to implied volatility surface under volatility models
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Monte Carlo calibration to implied volatility surface under volatility models

机译：蒙特卡罗在波动模型下校准隐含的挥发性表面

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AbstractThe calibration problem of implied volatility surface under complex financial models can be formulated as a nonlinear high-dimensional optimization problem. To resolve this problem for genuine volatility models, we develop a sequential methodology termed two-stage Monte Carlo calibration method. It consists of the first stage-dimension separation for splitting parametric set into two subsets, and the second stage-standard error reduction for efficient evaluation of option prices. The first stage dimension separation aims to reduce dimensionality of the optimization problem by estimating some volatility model parametersa prioriunder the historical probability measure such that the total number of model parameters under an option pricing measure is significantly reduced. The second stage standard error reduction aims simultaneously to reduce variance of option payoffs by the martingale control variate algorithm, and to increase the total number of Monte Carlo simulation by the hardware graphics processing unit (GPU) for parallel computing. This two-stage Monte Carlo calibration method is capable of solving a variety of complex volatility models, including hybrid models and multifactor stochastic volatility models. Essentially, it provides a general framework to analyze backward information from the historical spot prices and the forward information from option prices.]]>
机译：<！[cdata [<标题>抽象 ara id =“par1”>复杂金融模型下隐含波动表面的校准问题可以制定为非线性高维优化问题。为了解决真正的波动性模型的这个问题，我们开发了一种称为两级蒙特卡罗校准方法的顺序方法。它包括用于将参数分成两个子集的第一级尺寸分离，以及减少第二级标准误差，以便有效地评估选项价格。第一阶段尺寸分离旨在通过估计一些挥发性模型参数<重点型=“斜体”>在历史概率测量下的优先级=“斜体”，使得选项定价下的模型参数总数措施显着降低。第二阶段标准误差减少目的是通过Martingale控制变化算法减少期权收益的方差，并通过硬件图形处理单元（GPU）来增加用于并行计算的Monte Carlo模拟总数。这种两级蒙特卡罗校准方法能够解决各种复杂的波动模型，包括混合模型和多因素随机挥发性模型。基本上，它提供了一般框架，以分析来自历史点价格和期权价格的前向信息的落后信息。]>

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