3. All these paths are equally likely.PeriodPath0-11-22-3115.0%16.0%14.4%215.0%16.0%12.0%315.0%11.5%12.0%415.0%11.5%10.0%Step-2: For each interest rate path (the following calculation illustrates the valuation procedure for the second interest rate path, i.e. 15.0%, 16.0% and 12.0%), obtain the value of the bond as described under:Let Vij be the value of the bond in the ith period if its rating is j. At maturity, the bonds value is Rs. 112 if its rating is A, B or C and Rs. 40 if the rating is D.For valuing the bond in period 2, we use the risk-neutral transition matrix from period-2 to period-3. So, V2A is obtained as (7)Here 12.0% is the interest rate for period 3 in the first interest rate path. Similarly other V2j are obtained. Since there is a prepayment option we compare the value of the bond with the prepayment amount Rs. 98. If the value of the bond V2j is greater than the prepayment amount, the issuer is likely to prepay. V2A, V2B and V2C are 99.03, 96.67 and 90.42 respectively. Since V2A is greater than Rs. 98 (the prepayment amount), the issuer will exercise the prepayment option and the value of the bond will become Rs. 98. Since default is an absorbing state, the risk-neutral transition matrix indicates that the probability of migrating to any other state from a state of default is zero. Hence, the value of the bond at the default node is simply the present value of Rs. 40 received at the end of the original maturity period, the interest rate tree providing the discount rates.At this point, the coupon payment will be received, and the value of the bond will be incremented by Rs. 12, except in case of default, where no cash flow occurs.V2A, V2B V2C and V2D can then be used to compute V1A, V1B V1C and V1D in a similar fashion, except that the interest rate applicable will be r12 along the chosen interest rate path. (8)This procedure is repeated till the current period is reached. At this point, the credit rating applicable ...
