Fourier Analysis of India's Implied Volatility Index

Indian Journal of Finance, Vol.8, No. 10, October 2014, pp. 7-19

21 Pages Posted: 25 Oct 2014 Last revised: 14 Jun 2016

See all articles by Ronald T. Slivka

Ronald T. Slivka

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Chun Chang

New York University (NYU) - NYU Polytechnic School of Engineering

Sharon Yu

New York University (NYU) - NYU Polytechnic School of Engineering

Date Written: June 19, 2014

Abstract

The objective of this study was to analyze and model periodic behavior observed in India’s Nifty 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 trendline 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 shows surprising accuracy in identifying the temporal location of VIX peaks and troughs. The probable origin of one recurring VIX calendar frequency is traced to India’s earnings release cycle.

Keywords: Nifty, Nifty VIX, Fourier Analysis, Calendar Effects, Implied Volatility

JEL Classification: G12, G 13, G14, G15, G17

Suggested Citation

Slivka, Ronald T. and Chang, Chun and Yu, Xueting, Fourier Analysis of India's Implied Volatility Index (June 19, 2014). Indian Journal of Finance, Vol.8, No. 10, October 2014, pp. 7-19 , Available at SSRN: https://ssrn.com/abstract=2514444

Ronald T. Slivka (Contact Author)

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States
2153213524 (Phone)

Chun Chang

New York University (NYU) - NYU Polytechnic School of Engineering ( email )

Brooklyn, NY 11201
United States

Xueting Yu

New York University (NYU) - NYU Polytechnic School of Engineering ( email )

Brooklyn, NY 11201
United States

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