VOLATILITY SMILES AND VEGA-NEUTRALITY: ANALYSIS OF STRATEGIES IN THE OPTIONS MARKET FOR HEDGING AGAINST VOLATILITY RISK

This thesis aims to explore the concept of volatility in the options market, but also to mainly analyze how traders use daily quantitative and graphical methods to rebalance their option portfolios so to be exposed as less as possible to the volatility of the underlying assets. In the first Chapter, a brief introduction is made of the financial derivatives, i.e. forwards and futures and then, more so, of options. In the second Chapter we will introduce the most important framework in the world of options, i.e. the Black and Scholes model, analyzing the basic formulas and we will see the interpretation, starting to understand how in the options’ world volatility plays a key role differently from how it affects the markets of stocks and bonds. In the third Chapter we will give the definition of implied volatility of an option and we will develop an introduction to the famous Greeks, that is the various sensitivities of the option prices to the variation of the parameters from which the option’s value depends. Moreover we will see how two of them, theta and gamma, are at the base of options trading. In the fourth Chapter we will review the graphical shapes of the volatility smile, of the volatility term structure and of the volatility surface. Finally, in the fifth Chapter we will discuss about some of the strategies that options traders use to build vega-neutral portfolios, i.e. portfolios that are not exposed to the volatility of the underlying assets, using the volatility surface structure.