论文标题
短期渐近造型，用于非自相似随机波动率模型
Short-time asymptotics for non self-similar stochastic volatility models
论文作者
论文摘要
我们为随机波动率模型提供了短时大偏差原理（LDP），在该模型中，波动率表示为Volterra过程的函数。该南股自由营不需要在Volterra过程上进行严格的自相似性假设。因此，我们能够将这种LDP应用于两个非相似的粗糙波动率模型的两个值得注意的例子：模型，其中波动率是对数折叠的分数布朗运动的函数[Bayer et es fim of log-od-od of to log od-of thoim of log od of to的brownian运动的函数[Bayer等人，对数模拟的粗糙随机波动率模型。暹罗J.融资。 Math，2021，12（3），1257-1284]，以及它作为分数Ornstein-uhlenbeck（FOU）过程的函数给出的模型[Gaetchal等人，挥发性是粗糙的。量子。金融，2018，18（6），933-949]。在这两种情况下，我们都会对欧洲期权价格，隐含波动表面和隐含波动性偏斜产生后果。在FOU情况下，我们还讨论了中等偏差的定价和仿真结果。
We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra process. For this reason, we are able to apply such an LDP to two notable examples of non self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J. Financ. Math, 2021, 12(3), 1257-1284], and models where it is given as a function of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al., Volatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases we derive consequences for short-maturity European option prices, implied volatility surfaces and implied volatility skew. In the fOU case we also discuss moderate deviations pricing and simulation results.
