带反射的随机波动率模型的大偏差原理及Stein和Stein模型的三面
Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model
摘要：
引入了随机波动率模型，其中波动率由一个反射扩散的时间依赖非负函数描述。由于经典的Stein和Stein模型中存在一定的波动率设定错误，因此产生了使用反射扩散作为波动率构建块的想法。这个模型的一个版本，使用反射的Ornstein-Uhlenbeck过程作为波动率过程是一个特殊的例子，随机波动率模型的反射。本文的主要结果是在较弱的限制条件下，得到了带反射的随机波动率模型中对数价格过程的样本路径和小噪声大离差原理。我们利用这些结果研究了小噪声条件下二元障碍期权和看涨期权价格的渐近行为。
英文摘要：
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.
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