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.
Highlights
When a firm needs money, it can turn to its bank which lends it against, for example, periodic payments in a form of a loan
The balance of the paper is as follows: in the remainder of this section (Section 1.1) we review the related existing literature; in Section 2, we consider that the liquidity cost is negligible and that the borrower credit risk is defined by his/her default intensity which follows a CIR stochastic process
To approximate the PDE satisfied by the prepayment option, they define two state variables. Their approach is based on a bivariate binomial option pricing technique with a stochastic interest rate and a stochastic house value
Summary
When a firm needs money, it can turn to its bank which lends it against, for example, periodic payments in a form of a loan. The balance of the paper is as follows: in the remainder of this section (Section 1.1) we review the related existing literature; in Section 2, we consider that the liquidity cost is negligible and that the borrower credit risk is defined by his/her default intensity (called in the following “intensity”) which follows a CIR stochastic process In this situation, we are able to obtain a quasianalytic formula for the PVRP. Their approach is based on a bivariate binomial option pricing technique with a stochastic interest rate and a stochastic house value Another contribution by Cossin and Lu [1] applies the binomial tree technique (but it is time consuming for long-term loans due to the nature of binomial trees) to corporate loans. We refer to [18] for theoretical results concerning the pricing of American options in general
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