Embedded options in Mortgages: Implementation of the "Black, Derman and Toy" Model in the Italian Banking Industry

We analyze the variables determining the exercise of the prepayment option in mortgages for the Italian banking industry. We first examine the main studies on the valuation of mortgages and mortgage-backed securities (Sharp et al., 2008; Boudoukh et al., 1995; Black et al., 1990). We then apply a specific model to measure the prepayment option in the case of a refinancing option exercise. We consider a fixed-rate mortgage and try to estimate the exposure of a selected bank to interest rate risk. ALM studies have recognized the importance of this issue for financial intermediaries, especially for banks (Kalotay et al., 2007; Staikouras, 2006). Our main findings highlight that an increase in volatility causes an increase in option prices and a decrease in the mortgage market value. Moreover, the reduction of the positive gradient of the yield curve determines an increase in the prepayment option price. In the case of a yield curve with a marked positive gradient, the prepayment option price exhibits high sensitivity to volatility changes; and the mortgage value market reacts similarly. Finally, we observe that the prepayment option price can be considered a decreasing function of the credit spread and of the transaction costs.