Tesi di LAUREA SPECIALISTICA Titolo Opzioni di Prepayment nei Mutui Data 2012-04-23 Autore/i Cassaro, Alessandro Relatore Sgarra, C. Relatore Baviera, R. Full text non disponibile Abstract The aim of this work is to present a new procedure for pricing prepayment options related to callable products. The analysis is carried out in the mortgage market context in which the possibility of paying o the loan before the expiration leads to a signicant callability risk for the lender. In the italian market, the prepayment option was introduced by law in 2007 and at present is getting more and more relevant, being exercised in nearly half the cases. The pricing of this option is thus necessary in order to determine the correct spread that should be applied to the mortgage. The prepayment option is, in fact, a Bermudan swaption that could be dened on an amortising notional, depending on the mortgage features. In this work, the Bermudan option price is calculated in two ways: with a trinomial tree technique and using Montecarlo simulations. The first method is applied to the G2++ model, which is equivalent to the Hull-White two-factor model but it is easier to implement in practice. The model is calibrated with a new approach based on an approximated Black formula for pricing swaptions, which proves to be very accurate. This technique is more ecient than current implementations of the algorithm which imply two- dimension integration or tree-based pricing even for the calibration. A new approach is developed also for the trinomial tree pricing method, avoiding the numerical integration of the short rate, which is currently used in this algorithm. The whole procedure leads to very accurate results while reducing the computational costs if compared to current versions of the algorithm. The second procedure for pricing the Bermudan option is dened on the multi-factor dynamics of the Libor Market Model and thus implemented using Montecarlo simulations. A lower and an upper bound on the price are respectively calculated with the Longsta-Schwartz and Andersen- Broadie methods. In both cases the option value is determined at each time using a linear combination of basis functions; Montecarlo simulations allow to estimate the basis coefficients through backward induction. The lower bound is given by the option value at the initial time while the upper one is obtained by means of specic processes depending on the lower bounds at each time. The analysis of the basis coecients shows their big instabilities challenging the validity of the Longsta-Schwartz method in the multidimensional case. A comparison between the two pricing algorithms highlights the advantages of the trinomial tree method based on the G2++ model as an easy to implement, accurate and efficient procedure. The mortgage spread component related to the prepayment option price proves to be quite significant, stressing the importance of an adequate risk management of the callable feature.