Fourier Analysis of India's Implied Volatility Index

Abstract

The objective of this study was to analyze and model periodic behavior observed in India's Nifty Implied Volatility (VIX) Index and to seek the origins of these previously unreported calendar variations. Implied volatility and its variations are important to understand as the pricing of many financial assets and derivatives depend upon this variable. A novel modeling approach to this task uses Fourier analysis for the first time in the literature of implied volatility and calendar effect modeling. For this purpose, daily closing levels for the Nifty VIX Index were gathered covering trading days from 2010 through January 2014. Time series of VIX levels after removing a trend line were tested for normality, stationarity, and autocorrelation. Nifty index and Nifty VIX data were also tested for two-way Granger causality. Detrended Nifty VIX levels were Fourier analyzed to determine primary Fourier frequencies contributing to VIX periodic behavior. A Fourier model of VIX movements was constructed using four primary frequencies from the Fourier power spectrum. This model showed surprising accuracy in identifying the temporal location of VIX peaks and troughs. The probable origin of one recurring VIX calendar frequency was traced to India's earnings release cycle.