QUESTION 2 1. 25% Describe the historical evolution of Gaussian short rate modelling from the Merton model to the Hull and White two factors model, recalling for each model the short rate dynamics, the main characteristics, the shortcomings and the advantages. 2. 25% Show how to find a closed-form formula for the price of a bond in a short rate model with dynamics dr = u dt+odW, and compute the numeric value of a 3y maturity bond when u=0.02, 0 = 0.15, ro = 0.03. 3. 25% Given that the 6m and 18m discount factors are 0.99 and 0.96, illustrate how to interpolate, using the constant forward rate method the 12m discount factor. 4. 25% Consider a structured product paying at each reset date the amount max(LIBOR 1%,0) where LIBOR is the LIBOR rate with tenor equal to the coupon tenor. We decide to price the bond using Monte Carlo simulation. Detail all the needed steps in order to perform the assigned task. QUESTION 2 1. 25% Describe the historical evolution of Gaussian short rate modelling from the Merton model to the Hull and White two factors model, recalling for each model the short rate dynamics, the main characteristics, the shortcomings and the advantages. 2. 25% Show how to find a closed-form formula for the price of a bond in a short rate model with dynamics dr = u dt+odW, and compute the numeric value of a 3y maturity bond when u=0.02, 0 = 0.15, ro = 0.03. 3. 25% Given that the 6m and 18m discount factors are 0.99 and 0.96, illustrate how to interpolate, using the constant forward rate method the 12m discount factor. 4. 25% Consider a structured product paying at each reset date the amount max(LIBOR 1%,0) where LIBOR is the LIBOR rate with tenor equal to the coupon tenor. We decide to price the bond using Monte Carlo simulation. Detail all the needed steps in order to perform the assigned task