Valuation of the prepayment option of a perpetual corporate loan
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. Two frameworks are discussed: first a constant interest rate and a secondly a multi-regime framework where the interest rate is augmented by a liquidity factor 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. We establish in the unique regime case analytic formulas for the payoff of the option; in both cases we give a verification result that allows to compute 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 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 findings.
|Date of creation:||2013|
|Date of revision:|
|Publication status:||Published in Abstract and Applied Analysis, 2013, Vol. 2013|
|Contact details of provider:|| Web page: http://www.dauphine.fr/en/welcome.html|
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- Jimmy E. Hilliard & James B. Kau & V. Carlos Slawson, 1998. "Valuing Prepayment and Default in a Fixed-Rate Mortgage: A Bivariate Binomial Options Pricing Technique," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 26(3), pages 431-468.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
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