论文标题
具有反射的随机波动率模型的大偏差原理和Stein和Stein模型的三个面
Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model
论文作者
论文摘要
我们引入了随机波动率模型，其中波动率通过反射扩散的时间依赖性非负功能来描述。使用反映扩散作为波动率的基础的想法，由于经典的Stein和Stein模型中的一定波动率错误。该模型的一个版本使用反射的Ornstein-uhlenbeck过程作为波动率过程，是带有反射的随机波动率模型的一个特殊示例。本文在本文中获得的主要结果是在相当轻微的限制下反射的随机波动率模型中对数价格过程的样本路径和小差偏差原理。我们使用这些结果来研究二元障碍选项的渐近行为，并在小噪声制度中呼叫价格。
We introduce stochastic volatility models, in which the volatility is described by a time-dependent nonnegative function of a reflecting diffusion. The idea to use reflecting diffusions as building blocks of the volatility came into being because of a certain volatility misspecification in the classical Stein and Stein model. A version of this model that uses the reflecting Ornstein-Uhlenbeck process as the volatility process is a special example of a stochastic volatility model with reflection. The main results obtained in the present paper are sample path and small-noise large deviation principles for the log-price process in a stochastic volatility model with reflection under rather mild restrictions. We use these results to study the asymptotic behavior of binary barrier options and call prices in the small-noise regime.
