On smile properties of volatility derivatives and exotic products:\n understanding the VIX skew

2018/08/10 by Elisa Alòs, Alòs, Elisa, David García-Lorite +3
Economics, Econometrics and Finance · #60H07 #91G20 #91G80 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1808.03610

openalex publication_date 2018/08/10 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

We develop a method to study the implied volatility for exotic options and\nvolatility derivatives with European payoffs such as VIX options. Our approach,\nbased on Malliavin calculus techniques, allows us to describe the properties of\nthe at-the-money implied volatility (ATMI) in terms of the Malliavin\nderivatives of the underlying process. More precisely, we study the short-time\nbehaviour of the ATMI level and skew. As an application, we describe the\nshort-term behavior of the ATMI of VIX and realized variance options in terms\nof the Hurst parameter of the model, and most importantly we describe the class\nof volatility processes that generate a positive skew for the VIX implied\nvolatility. In addition, we find that our ATMI asymptotic formulae perform very\nwell even for large maturities. Several numerical examples are provided to\nsupport our theoretical results.\n

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• Asymptotic behaviour of the fractional Heston model

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