Modeling the Dynamics of Implied Volatility Surface of S&P CNX NIFTY

This study is intended to apply and extend the accepted implied volatility modelling principles to the S&P CNX NIFTY (Index from National Stock Exchange of India - NSE) index options and account for the deviations in the volatility surface and the corresponding risk factors. The methodology followed for modelling implied volatility is similar to Dumas, Fleming and Whaley (DFW 1998) and Ishan Ullah Badshah (IUB – working paper 2008) and the methodology used for Principal Component Analysis is similar to the one applied by Skiadopolous, Hodges and Clewlow (SHC 1999). We compare the implied volatility surface generated using one linear model (constant volatility) and three nonlinear models that take into consideration varying levels of skew or smile and maturities. We find that the fourth model best captures all the characteristics of implied volatility. Secondly, we apply Principal Component Analysis (PCA) to the implied volatility surface and extract the most relevant principal components that explain most of the dynamics of the volatility surface. We determined that 80.66% to 94.47% of the variation in the IV surface is explained by the first three principal components. Lastly, we study the behaviour of the implied volatility surface of the S&P CNX NIFTY for two distinct periods – pre crisis (2006) and post crisis (2009). Specific applications of the model include pricing and hedging of derivatives and risk management