Modelování volatility smile pomocí lineární regrese průřezových dat parametrů gamma, vanna a volga

This master’s thesis examines the modelling of cross-sectional structure of option-implied volatility using risk exposures gamma, vanna and volga expressed in their cash forms. The objective is to empirically investigate whether the market-observed implied volatility smile can be reconstructed through a cross-sectional regression of option time decay on these nonlinear risk exposures. The empirical analysis is conducted using S&P 500 (SPX) option data covering multiple market snapshots and maturities ranging from short-term to long-term expirations. Several regression specifications are compared, differing primarily in the use of reduced and unreduced model forms, the definition of the at-the-money boundary, and the selection of options included in the regression. The results show that the cross-sectional structure of implied volatility can be approximated relatively well using the selected cash Greek exposures. The best performance is achieved by the unreduced specification using the forward price as the at-the-money boundary and all available options within each expiration. The results further indicate that model accuracy depends on the particular shape of the volatility smile and tends to deteriorate for curves exhibiting more pronounced local nonlinearities.