Power law in Sandwiched Volterra Volatility model

2023/11/02 by Giulia Di Nunno, Di Nunno, Giulia, Anton Yurchenko-Tytarenko +1
Economics, Econometrics and Finance · #60G22 #60H10 #60H35 #91G30 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2311.01228

openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present analytical proof demonstrating that the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behavior of the at-the-money implied volatility skew, provided the correct choice of the Volterra kernel. To obtain this result, we assess the second-order Malliavin differentiability of the volatility process and investigate the conditions that lead to explosive behavior in the Malliavin derivative. As a supplementary result, we also prove a general Malliavin product rule.

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