Dynamics of the volatility surface

Abstract

Our project aims to analyze the volatility surface observed in options market. The intricacies of the volatility surface have challenged the traders and academicians across the world for the last 25 years. In our project, we have explored some of these challenges and their consequences. We started by examining the volatility smile exhibited across different asset classes. The market quoting conventions of the FX markets are studied in detail, and the volatility greeks are defined. Since the Black Scholes model fails to incorporate the volatility smile, traders have developed complex procedures to value and hedge the options. The Vanna Volga method - one such model to correct the Black Scholes pricing of options, is discussed in the report. Next we have explored the popular methods of modelling the volatility smile. The local volatility models and the stochastic volatility models are intuitively analyzed and their advantages and limitations are discussed. In the final part of our project we have implemented the local volatility model for the Indian equity options (CNX NIFTY Index). We have checked the consistency of the model by using it to compute the European option prices and comparing it with the available market data. The results of our project are presented in the report.