Valuation of the Prepayment Option of a Perpetual Corporate Loan

Abstract

We investigate in this paper a perpetual prepayment option related to a corporate loan. The default intensity of the firm is supposed to follow a CIR process. We assume that the contractual margin of the loan is defined by the credit quality of the borrower and the liquidity cost that reflects the funding cost of the bank. Two frameworks are discussed: firstly a loan margin without liquidity cost and secondly a multiregime framework with a liquidity cost dependent on the regime. The prepayment option needs specific attention as the payoff itself is an implicit function of the parameters of the problem and of the dynamics. In the unique regime case, we establish quasianalytic formulas for the payoff of the option; in both cases we give a verification result that allows for the computation of the price of the option. Numerical results that implement the findings are also presented and are completely consistent with the theory; it is seen that when liquidity parameters are very different (i.e., when a liquidity crisis occurs) in the high liquidity cost regime, the exercise domain may entirely disappear, meaning that it is not optimal for the borrower to prepay during such a liquidity crisis. The method allows for quantification and interpretation of these findings.

Prepayment Option of a Perpetual Corporate Loan: The Impact of the Funding Costs

“…The pricing of a simplified one-dimensional model with constant interest rate was proposed in [39]. With respect to this first work the present contribution does not only investigate the non-trivial dynamics of the interest rate but also proposes an adequate numerical algorithm (in Section 3) that requires at its turn the introduction of adapted functional spaces.…”

The Liquidity Regimes and the Prepayment Option of a Corporate Loan in the Finite Horizon Case

“…The pricing of a simplified one-dimensional model was proposed in an infinite horizon (perpetual) setting in Papin and Turinici (2013). In Papin and Turinici (2014) it is investigated in addition a non-trivial dynamics of the interest rate and a numerical algorithm is proposed together with the introduction of adapted functional spaces.…”