Pricing CAT futures in a stochastic volatility setting: an extension to the Italian weather market

This thesis develops a pricing framework for Cumulative Average Temperature (CAT) futures in the context of stochastic volatility and applies it to the Italian weather market. The study extends existing models by incorporating a seasonal stochastic volatility component using the Barndorff-Nielsen and Shephard (BNS) model and develops a new class of risk-neutral measures using a combination of the Esscher and Girsanov transforms. An empirical analysis is conducted using temperature data from four Italian cities, and a simulation is performed to derive prices for synthetic CAT futures contracts. The proposed model is demonstrated to successfully capture the seasonal dynamics and volatility observed in temperature data, thereby providing a robust tool for the hedging of temperature risks, particularly in the context of rising climate uncertainty.