Short-time implied volatility of additive normal tempered stable processes

Michele Azzone; Roberto Baviera

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arXiv · 2108.02447

Short-time implied volatility of additive normal tempered stable processes

Michele Azzone·Roberto Baviera

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Abstract

Empirical studies have emphasized that the equity implied volatility is characterized by a negative skew inversely proportional to the square root of the time-to-maturity. We examine the short-time-to-maturity behavior of the implied volatility smile for pure jump exponential additive processes. An excellent calibration of the equity volatility surfaces has been achieved by a class of these additive processes with power-law scaling. The two power-law scaling parameters are $\beta$, related to the variance of jumps, and $\delta$, related to the smile asymmetry. It has been observed, in option market data, that $\beta=1$ and $\delta=-1/2$. In this paper, we prove that the implied volatility of these additive processes is consistent, in the short-time, with the equity market empirical characteristics if and only if $\beta=1$ and $\delta=-1/2$.

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Michele Azzone, Roberto Baviera. 2021-08-05. Short-time implied volatility of additive normal tempered stable processes. https://arxiv.org/abs/2108.02447

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