ond with Prepayment OptionSo far, interest rate risk has not been relevant to the valuation of any of the loan or derivative products. However, in case of a loan with an embedded prepayment option, the interest rate volatility needs to be considered. It is here that our model departs from presently available models in giving a framework to price prepayment options embedded in loans. To understand the justification for using the interest rate tree, let us examine the drivers that lead the borrower to prepay the loan:Fall in interest rates: With a fall in interest rates, a borrower can obtain cheaper funding in the market, and hence would be motivated to prepay the current (fixed rate) loan.Improvement in credit rating: As spreads narrow with enhancement in credit rating, borrowers with rating upgrades are driven to opt for the prepayment because they too can obtain refinance at cheaper rates now.However, the decision to prepay is not independently determined by interest rate decline and credit rating upgradation. In some situations, the changes in interest rate and in credit ratings could exert opposite influences on the decision to prepay. Hence, we need to consider the simultaneous impact of changes in interest rates and credit ratings on the valuation of the bond. We shall value the loan (& the embedded option) using a backward recursive method for computing the expected present value of the loan in a risk-neutral world. In order to move into a risk-neutral framework with respect to interest rates, we have used a recombining binomial interest rate tree (refer Chart-1). Chart-1The Risk-Neutral Interest Rate TreeConsider a 12% coupon bond rated B with a maturity of 3-periods. Let us suppose the issuer has the option to prepay starting from the first period. The prepayment amount is fixed at Rs. 98. The steps in the valuation of the bond and the embedded option are: Step-1: List all possible interest rate paths from period 0 to period ...
