Athos Brogi

PhD thesis: "A Binomial Tree to Price European Options".

A binomial tree is presented and implemented to price European options written on S&P 500 index.

The tree is utilized to model implied volatility smile and surface, comparing them to benchmark B-S implied smile and surface.

The tree can model the implied volatility surface, where three option expiry dates with three months between them are considered, without the need to change the values of the tree's parameters.

Returns on S&P 500 index are simulated using tree, and tree's simulated returns distribution accounts for excess kurtosis of empirical returns distribution.

Another binomial tree is created, and its simulated returns distribution captures both skewness and excess kurtosis of empirical returns distribution.