An Empirical Model of India's Nifty VIX Index

Abstract

As implied volatility is essential for pricing options, analyzing derivative strategies and measuring risk in investment portfolios containing derivatives, and understanding variations in implied volatility also becomes vital. Aside from a secular trend, volatility clustering and calendar effects are two commonly occurring sources of such variation. To analyze volatility clusters in India's implied volatility index (Nifty VIX), daily closing levels for the Nifty VIX were gathered covering trading days from January 2010 through January 2014. ARIMA and GARCH models applied to the de-trended Nifty VIX time series were found to be of limited use for describing this data with its episodic clustering and periodic events. However, an alternative modelling approach using Fourier analysis and Butterworth filters successfully split the time series into two logical parts, one with both clusters and periodic behavior and one with near-white noise. The likely origins of major clusters in India's Nifty implied volatility index appeared to be linked to important global financial events external to India during the study period, thereby supporting evidence of temporal spillover into the Indian market. The half-lives of implied volatility clusters were measured and compared with those in the U.S. market. The full range of Nifty VIX behavior for the study period was seen to consist of four distinct elements- trend, periodic events, clusters of volatility, and noise. When combined, these elements provided an empirical model able to produce successful forecasts for 60-day-ahead periods.