is known (B in the present illustration), and thus the bond value can be ascertained.A schematic representation of the backward recursion of the bond cash flows is shown below for the second interest rate path, i.e. r01 = 15%, r12 = 16%, and r23 = 12%, yielding the bond value (net of the value of the embedded prepayment option) to be Rs. 84.47.Strike price / Prepayment amount:98Period0123RatingA104.83110.00112B84.47101.47108.67112C94.10102.42112D30.7935.7140The value at each node includes the coupon received at that node.Step-3: Since we are operating in a risk neutral framework and each of the interest rate paths is equally likely, the value of the bond is the simple average of values obtained for each of the interest rate paths. Step-4: A similar exercise can be carried out to price a plain bond, i.e. where there are no embedded options. In this case, at each node, there would be no need to compare the amount arrived at by the backward recursion with any other amount, because there is no option available to exercise.Step-5: The difference between the two values (Step-3 and Step-4) represents the value of the embedded option. Table-7 contains an analysis of the price of the bond with a prepayment option into the price of a plain bond, and that of a prepayment option.Table-7Components of the price of a bond with an embedded prepayment optionr01r12r23Bond value with embedded optionValue of plain bondValue of embedded prepayment option15.0%16.0%14.4%83.2183.210.0015.0%16.0%12.0%84.4784.610.1415.0%11.5%12.0%87.4887.630.1515.0%11.5%10.0%88.3188.890.58Price of instrument85.8786.090.227.CONCLUSIONA loan or a bond can be viewed as a portfolio of a risk-free instrument and a credit derivative that pays an amount equal to the loss in the event of default. This gives a powerful framework to split up the loan price into its building blocks - a time value of money (represented by the risk-free rate), and a risk premium (for bearing credit risk).Asc...
