Valuation of the prepayment option of a perpetual corporate loan
Résumé
We investigate in this paper a perpetual prepayment option related to a corporate loan. The default intensity of the rm is supposed to follow a CIR process. We assume the contractual margin of the loan is de ned by the credit quality of the borrower and the liquidity cost that re ects the funding cost of the bank. Two frameworks are discussed: rstly a loan margin without liquidity cost and secondly a multi-regime framework with a liquidity cost dependent on the regime. The prepayment option needs speci c attention as the payo itself is an implicit function of the parameters of the problem and of the dynamics. In the unique regime case, we establish quasi analytic formulas for the payo of the option; in both cases we give a veri cation result that allows to compute the price of the option. Numerical results that implement the ndings are also presented and are completely consistent with the theory; it is seen that when liquidity parameters are very di erent (i.e., when a liquidity crisis occur) 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 to quantify and interpret these ndings.
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