论文标题
多元随机波动率模型和较大的偏差原理
Multivariate Stochastic Volatility Models and Large Deviation Principles
论文作者
论文摘要
我们建立了一个综合样本路径大偏差原理（LDP），用于与多元抗时期随机波动率模型相关的对数过程。新的LDP保留的模型示例包括高斯模型，非高斯分数模型，混合模型，具有反射的模型以及波动率过程是对Volterra型随机积分方程的解决方案的模型。日志过程的LDP用于获得大型偏差样式渐近公式，用于从开放式设置的日志过程的第一个退出时间和多维二进制屏障选项的价格。我们还证明了volterra型随机积分方程的溶液的样本路径LDP具有可预测的系数，具体取决于辅助随机过程。
We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models, non-Gaussian fractional models, mixed models, models with reflection, and models in which the volatility process is a solution to a Volterra type stochastic integral equation. The LDP for log-processes is used to obtain large deviation style asymptotic formulas for the distribution function of the first exit time of a log-process from an open set and for the price of a multidimensional binary barrier option. We also prove a sample path LDP for solutions to Volterra type stochastic integral equations with predictable coefficients depending on auxiliary stochastic processes.
