Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models
Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models
复制标题
仿射随机波动率模型的长期轨迹大偏差和重要性采样
DOI：
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发表时间：
2021
影响因子：
1.2
通讯作者：
P. Tankov
中科院分区：
文献类型：
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作者：
Z. Grbac;David Krief;P. Tankov
摘要针对Keller-Ressel（2011）提出的仿射随机波动率模型，建立了一个路径方向的大偏差原理，并将其应用于这些模型中路径依赖期权价格的Monte Carlo计算，推广了Genin和Tankov（2020）针对指数Lévy模型的方法.为此，我们应用指数仿射测度变化，并以Guasoni和Robertson（2008）和Robertson（2010）的方式使用Varadhan引理来近似寻找最小化Monte Carlo估计量方差的测度的问题。我们测试的赫斯顿模型和无跳跃的方法，以证明其数值效率。
Abstract We establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.