英文标题：
《Large deviation principle for Volterra type fractional stochastic
volatility models》
---
作者：
Archil Gulisashvili
---
最新提交年份：
2018
---
英文摘要：
We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\\sigma$ of a continuous Gaussian process $\\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $\\sigma$ is globally H\\\"{o}lder-continuous and the process $\\widehat{B}$ is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on $\\sigma$ and $\\widehat{B}$. We assume that $\\sigma$ satisfies a mild local regularity condition, while the process $\\widehat{B}$ is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process $\\widehat{B}$, we derive a large deviation principle in the small-time regime. As an application, we obtain asymptotic formulas for binary options, call and put pricing functions, and the implied volatility in certain mixed regimes.
---
中文摘要：
我们研究了分数阶随机波动率模型，其中波动率过程是连续高斯过程的正连续函数$\\ sigma$。Forde和Zhang在这样一个模型中建立了对数价格过程的大偏差原理，假设函数$\\ sigma$是全局H{o}lder连续的，过程$\\ widehat{B}$是分数布朗运动。本文在$\\ sigma$和$\\ widehat{B}较弱的限制下，证明了类似的小噪声大偏差原理$. 我们假设$\\ sigma$满足一个温和的局部正则条件，而过程$\\ widehat{B}$是一个Volterra型高斯过程。在过程$\\widehat{B}的自相似性的另一个假设下，我们导出了小时间范围内的大偏差原理。作为应用，我们得到了二元期权、看涨期权和看跌期权定价函数的渐近公式，以及某些混合制度下的隐含波动率。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->