Valuation of the Prepayment Option of a Perpetual Corporate Loan

Timothée Papin (1) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We investigate in this paper a perpetual prepayment option related to a corporate loan.The default intensity of the firmis 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.

Mots clés: Markov modulated dynamics.; liquidity regime; loan prepayment; mortgage option; American option; perpetual option; option pricing; Snell envelope; prepayment option; CIR process; switching regimes; Markov modulated dynamics

Domaines: Analyse numérique [math.NA]; Economies et finances; Finance quantitative [q-fin.CP]; Gestion des risques [q-fin.RM]; Pricing [q-fin.PR]

Timothée Papin, Gabriel Turinici. Valuation of the Prepayment Option of a Perpetual Corporate Loan. Abstract and Applied Analysis, 2013, 2013, pp.960789. ⟨10.1155/2013/960789⟩. ⟨hal-00653041v4⟩