Modelling and Numerics of S&P CNX Nifty Index Option Implied Volatility Surface

In this paper, we propose a new model for constructing well-behaved and smooth implied volatility surface. There are three basic challenges in constructing well-behaved and smooth implied volatility surface. First, the implied volatility is known only for unevenly distributed discrete sparse set of signifi cantly traded strike prices and time to maturity. Second, implied volatility function should not allow for arbitrage. And third, implied volatility function should be having at least second order regularity with respect to strike price and first order regularity with respect to time to maturity. To address above stated challenges, we propose a new model which combines non parametric method and interpolation technique that gives more accurate and realistic volatility surface. Comparative study on S&P CNX NIFTY index option data show the advantage of using this new approach over parametric and non-parametric models reported in literature