Explicit formulas for pricing of callable mortgage-backed securities in a case of prepayment rate negatively correlated with interest rates

In this paper, we deal with the pricing of Mortgage-Backed Securities (MBS) in the reduced-form framework. Based on the ideas presented by Brunel and Jribi (2008) [8] and Rom-Poulsen (2007) [7], we introduce a stochastic process Qt=e−∫0tλsds to model the prepayment factor and assume that the prepaym...

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Published inJournal of mathematical analysis and applications Vol. 393; no. 2; pp. 421 - 433
Main Authors Qian, Xiao-song, Jiang, Li-shang, Xu, Cheng-long, Wu, Sen
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2012
Subjects
Mortgage-backed securities
Prepayment factor
Prepayment risk
Reduced form model
Mortgage-backed securities
Reduced form model
Prepayment factor
Prepayment risk
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Summary:In this paper, we deal with the pricing of Mortgage-Backed Securities (MBS) in the reduced-form framework. Based on the ideas presented by Brunel and Jribi (2008) [8] and Rom-Poulsen (2007) [7], we introduce a stochastic process Qt=e−∫0tλsds to model the prepayment factor and assume that the prepayment rate λt is inversely proportional to the stochastic interest rate rt, which follows a CIR process. Explicit formulas for pass-through MBSs and semi-analytical solutions for Collateralized Mortgage Obligations (CMO) are obtained through PDE approaches. Based on the formulas, numerical results are provided to explain the dependence of MBS prices on mortgage parameters and the negative correlation between MBS prices and interest rates.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.03.057