We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options.

中文翻译：

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时间非均一的高斯随机波动率模型：较大的偏差和较高的粗糙度

我们介绍了时间不均匀的随机波动率模型，其中的波动率是通过Volterra型连续高斯过程的非负函数描述的，该函数可能具有非常粗糙的样本路径。本文获得的主要结果是在非常温和的约束下，在时间非均质的超粗糙高斯模型中，对数价格过程的样本路径和小噪声大偏差原理。我们使用这些结果来研究二元障碍期权，退出时间概率函数和看涨期权的渐近行为。