On the difference between the volatility swap strike and the zero vanna\n implied volatility

2019/12/11 by Elisa Alòs, Alos, Elisa, Frido Rolloos +3
Economics, Econometrics and Finance · #91G99 #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1912.05383

openalex publication_date 2019/12/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, Malliavin calculus is applied to arrive at exact formulas for\nthe difference between the volatility swap strike and the zero vanna implied\nvolatility for volatilities driven by fractional noise. To the best of our\nknowledge, our estimate is the first to derive the rigorous relationship\nbetween the zero vanna implied volatility and the volatility swap strike. In\nparticular, we will see that the zero vanna implied volatility is a better\napproximation for the volatility swap strike than the ATMI.\n

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