Pricing Prepayment Option in C&I Loans at Origination

This paper presents a pricing model of commercial and industrial (C&I) loan prepayment option. Modeling of prepayment is essential in pricing mortgage contracts since prepayment truncates the timing and amount of expected cash flows. Lenders normally charge a penalty for prepayment, for example interest on unused principal. We forst propose that prepayment penalties should be viewed as fees in arrears reflecting the value of a call option at origination. We then rationalize business prepayment behavior with both refinancing and non-refinancing incentives. Business borrowers make rationaldecisions toe rfinance when interest rates fall or their credit standing improves. Business borrowers also prepay with internal equity to optimize capital structure and reduce financing costs. Prepayment value in C&I loans reflects the option value depending on the market conditions, borrowers creditworthiness and the need to change capital structure and reduce costs. In the rest of the paper, we propose a contingent-claims approach to the pricing C&I loan prepayment contract, given loans being defaultable, and transaction costs and fees being proportional to the loan amount. An implementation example is provided with prepayment option value being determined via a double non-recombining tree. The two underlying state variables are forward credit spread and forward interest rate specified in the HJM framework and their volatilities are exponentially dampened and proportional to the spot rates. We find that prepayment option value concentrates on the first few periods, and locking out these periods would reduce the option value significantly. We also find that prepayment option value on a variable-rate loan is insensitive to the forward interest rate volatility but very sensitive to the forward credit spread volatility.