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粗糙波动率下特征函数的短时展开及其应用AI 解读

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an Itô semimartingale over a shrinking time interval. The spot characteristics of the Itô semimartingale are allowed to have dynamics of general form. In particular, their paths can be rough, that is, exhibit local behavior like that of a fractional Brownian motion, while at the same time have jumps with arbitrary degree of activity. The expansion result shows the…

粗糙波动率的非参数检验AI 解读

We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency…

利用期权估计波动率的波动率与杠杆效应AI 解读

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options' expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order…