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

Timothee Papin (1, 2) , Gabriel Turinici (3, 1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 BNP Paribas CIB Ressource Portfolio Management
3 IUF - Institut universitaire de France

We investigate the prepayment option related to a corporate loan. The default intensity of the firm is supposed to follow a Cox-Ingersoll-Ross (CIR) process and the short interest rate is assumed constant. A liquidity term that represents the funding costs of the bank is introduced and modeled as a continuous time discrete state Markov jump process. The prepayment option is an American option with the payoff being an implicit function of the parameters of the problem. We give a verification result that allows to compute the price of the option. Numerical results are completely consistent with the theory; it is seen that the exercise domain may entirely disappear during such a liquidity crisis meaning that it is not optimal for the borrower to prepay. The method allows to quantify and interpret these findings.

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

Domaines: Analyse numérique [math.NA]; Finance quantitative [q-fin.CP]; Pricing [q-fin.PR]

Timothee Papin, Gabriel Turinici. The Liquidity Regimes and the Prepayment Option of a Corporate Loan in the Finite Horizon Case. Global Credit Review, 2015, 5 (1), pp.19-33. ⟨10.1142/S2010493615500026⟩. ⟨hal-01073598v2⟩