The liquidity regimes and the prepayment option of a corporate loan in the finite horizon case

Timothée Papin (1) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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; Snell envelope; prepayment option; CIR process; switching regimes; Markov modulated dynamics

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

Timothée Papin, Gabriel Turinici. The liquidity regimes and the prepayment option of a corporate loan in the finite horizon case. 2014. ⟨hal-01073598v1⟩