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We valued an RMBS in class using Monte Carlo simulation. The RMBS has a par value of $1 million, a WAM of 10 years, a WAC of 8%, a pass-through rate of 8%, annual cash flows, a balloon payment at the...

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We valued an RMBS in class using Monte Carlo simulation. The RMBS has a par value of $1 million, a WAM of 10 years, a WAC of 8%, a pass-through rate of 8%, annual cash flows, a balloon payment at the end of the fourth year, and zero default risk. Figure 4.3 provides the binomial tree for the spot rates and the refinancing rates. Table 4.2 defines the 8 interest rate paths in terms of the refinancing rates. Table 4.4 provides the prepayment model.

(a) Calculate the cash flows for years 1, 2, 3, and 4 along path 6.

(b) The zero-coupon rates for years 1, 2, 3, and 4 along path 6 are 8.00%, 8.2996%, 8.1996%, and 8.2996%, respectively. Calculate the value of the RMBS for path 2.

simulation-problem-homework-4-cnfgrlfo.docx london0131962590galleyqxd-lzyyou1f-bg4sp1ft.pdf
Answered Same Day Nov 17, 2021

Solution

Himanshu answered on Nov 18 2021
120 Votes
Cash Flow 1
        1
        Par    $ 1,000,000.00
        Weighted Average Maturity    10    120    months
        Weighted Average Coupon    8%
        P    82.42    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,133    I    $ 6,667    SP    $ 5,466    CPR    0.006    CF1    p+pp+I    B2 = B1-SP-PP    $ 994,035.27
                                SMM    0.0005013803        $ 19,298
                                PP    $ 498.64
        2
        Par    $ 994,035.27
        Weighted Average Maturity    10    119    months
        Weighted Average Coupon    8%
        P    81.97    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,127    I    $ 6,627    SP    $ 5,500    CPR    0.012    CF1    p+pp+I    B2 = B1-SP-PP    $ 987,541.48
                                SMM    0.0010055425        $ 19,748
                                PP    $ 994.01
        3
        Par    $ 987,541.48
        Weighted Average Maturity    10    118    months
        Weighted Average Coupon    8%
        P    81.52    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,114    I    $ 6,584    SP    $ 5,531    CPR    0.018    CF1    p+pp+I    B2 = B1-SP-PP    $ 980,525.30
                                SMM    0.0015125192        $ 20,183
                                PP    $ 1,485.31
        4
        Par    $ 980,525.30
        Weighted Average Maturity    10    117    months
        Weighted Average Coupon    8%
        P    81.06    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,096    I    $ 6,537    SP    $ 5,559    CPR    0.024    CF1    p+pp+I    B2 = B1-SP-PP    $ 972,994.26
                                SMM    0.0020223433        $ 20,605
                                PP    $ 1,971.72
        5
        Par    $ 972,994.26
        Weighted Average Maturity    10    116    months
        Weighted Average Coupon    8%
        P    80.60    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,072    I    $ 6,487    SP    $ 5,585    CPR    0.03    CF1    p+pp+I    B2 = B1-SP-PP    $ 964,956.76
                                SMM    0.0025350486        $ 21,011
                                PP    $ 2,452.43
        6
        Par    $ 964,956.76
        Weighted Average Maturity    10    115    months
        Weighted Average Coupon    8%
        P    80.14    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,041    I    $ 6,433    SP    $ 5,608    CPR    0.036    CF1    p+pp+I    B2 = B1-SP-PP    $ 956,422.05
                                SMM    0.0030506693        $ 21,401
                                PP    $ 2,926.66
        7
        Par    $ 956,422.05
        Weighted Average Maturity    10    114    months
        Weighted Average Coupon    8%
        P    79.67    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 12,004    I    $ 6,376    SP    $ 5,628    CPR    0.042    CF1    p+pp+I    B2 = B1-SP-PP    $ 947,400.23
                                SMM    0.0035692401        $ 21,774
                                PP    $ 3,393.61
        8
        Par    $ 947,400.23
        Weighted Average Maturity    10    113    months
        Weighted Average Coupon    8%
        P    79.20    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 11,962    I    $ 6,316    SP    $ 5,646    CPR    0.048    CF1    p+pp+I    B2 = B1-SP-PP    $ 937,902.19
                                SMM    0.0040907968        $ 22,130
                                PP    $ 3,852.53
        9
        Par    $ 937,902.19
        Weighted Average Maturity    10    112    months
        Weighted Average Coupon    8%
        P    78.73    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 11,913    I    $ 6,253    SP    $ 5,660    CPR    0.054    CF1    p+pp+I    B2 = B1-SP-PP    $ 927,939.64
                                SMM    0.0046153754        $ 22,468
                                PP    $ 4,302.65
        10
        Par    $ 927,939.64
        Weighted Average Maturity    10    111    months
        Weighted Average Coupon    8%
        P    78.26    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 11,858    I    $ 6,186    SP    $ 5,671    CPR    0.06    CF1    p+pp+I    B2 = B1-SP-PP    $ 917,525.07
                                SMM    0.0051430128        $ 22,787
                                PP    $ 4,743.24
        11
        Par    $ 917,525.07
        Weighted Average Maturity    10    110    months
        Weighted Average Coupon    8%
        P    77.78    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 11,797    I    $ 6,117    SP    $ 5,680    CPR    0.066    CF1    p+pp+I    B2 = B1-SP-PP    $ 906,671.70
                                SMM    0.0056737466        $ 23,087
                                PP    $ 5,173.58
        12
        Par    $ 906,671.70
        Weighted Average Maturity    10    109    months
        Weighted Average Coupon    8%
        P    77.30    Interest Payment         Scheduled Payment        Estimated Period        First Year Cash Flow        The Beginning balacne for the second month is
            $ 11,730    I    $ 6,044    SP    $ 5,685    CPR    0.072    CF1    p+pp+I    B2 = B1-SP-PP    $ 895,393.52
                                SMM    0.0062076148        $ 23,367
                                PP    $ 5,592.98
Cash Flow 2
        13
        Par    $ 895,393.52
        Weighted Average Maturity    10    108    months
        Weighted Average Coupon    8%
        P    76.81    Interest Payment         Scheduled Payment        Estimated Period        Second Year Cash Flow        The Beginning balacne for the second month is
            $ 11,657    I    $ 5,969    SP    $ 5,688    CPR    0.078    CF2    p+pp+I    B2 = B1-SP-PP    $ 883,705.17
                                SMM    0.0067446566        $ 23,627
                                PP    $ 6,000.76
        14
        Par    $ 883,705.17
        Weighted Average Maturity    10    107    months
        Weighted Average Coupon    8%
        P    76.32    Interest Payment         Scheduled Payment        Estimated Period        Second Year Cash Flow        The Beginning balacne for the second month is
            $ 11,578    I    $ 5,891    SP    $ 5,687    CPR    0.084    CF2    p+pp+I    B2 = B1-SP-PP    $ 871,622.00
                                SMM    0.0072849116        $ 23,866
                                PP    $ 6,396.29
        15
        Par    $ 871,622.00
        Weighted Average Maturity    10    106    months
        Weighted Average Coupon    8%
        P    75.83    Interest Payment         Scheduled Payment        Estimated Period        Second Year Cash Flow        The Beginning balacne for the second month is
            $ 11,494    I    $ 5,811    SP    $ 5,683    CPR    0.09    CF2    p+pp+I    B2 = B1-SP-PP    $ ...
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