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.
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