Ricerc@Sapienza

The present work aims at evaluating options using the Heston model. This model is presented both from a theoretical and a practical point of view. Initially, we review the salient mathematical steps that lead to its formulation. In particular, the hedging portfolio of the underlying asset price and variance is constructed in order to derive the exercise probability of the option.

The present work aims at evaluating Long-Term Care annuity contracts with Guaranteed Lifetime Withdrawal Benefits using the method of the Exact Individual Trajectories. This model, basically developed for the management of pension funds, is setup on an axiomatic basis and allows a complete description of the sample space. In addiction the financial component of the contract is modelled through the Heston model which considers stochastic both the stock price and the volatility.