5 Bonus- Stochastic Interest Rate Models (20 Points)This is a bonus question that requires working with stochastic interest rate models. In particular,you will be exposed to the famous Vasicek...

5 Bonus- Stochastic Interest Rate Models (20 Points)This is a bonus question that requires working with stochastic interest rate models. In particular,you will be exposed to the famous Vasicek (1977) model, which is considered the archetype of bondpricing models. You will need to refer to the discrete version of the model with respect to Section4.1 from Backus et al. (1998). Following the formulation of Backus et al. (1998), your main task isthe following:1. First, you need to replicate Figure 1 of Backus et al. (1998). Note that there is no need todownload the original data. You can reconstruct the figure using the the summary statisticsprovided in Table 1 of the paper.2. Second, the table below provides a sequence of 4 innovations foret+sfors= 1,2,3,4, whichcome fromN(0,1)distribution. Given these innovations, your final task is to simulate theyield curve over the next four periods. This should result in four yield curves. In line withFigure 1 from Backus et al. (1998), your summary should illustrate the four yield curves onthe same plot. Make sure to use a legend to denote which line is which.et+10.55et+2-0.28et+31.78et+40.19Note: Backus et al. (1998) discertize the model into monthly increments. Hence, the ultimategoal behind the above exercise to simulate the yield curve over 4 months. The major challengebehind this formulation is to construct the yield curve under no-arbitrage pricing. For a givenshort-term rate, i.e. 1-month Treasury yield, the no-arbitrage pricing dictates how the short-termrate propagate through the yield curve. Section 4.1 Backus et al. (1998) provides the closed-formsolution for this no-arbitrage yield curve