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Title: Intensity-based framework and penalty formulation of optimal stopping problems
Authors: Dai, Min
Kwok, Yue Kuen
You, Hong
Keywords: Linear complementarity formulation
Mortgage prepayment
Callable feature
Intensity approach
Penalty method
Event risk
Issue Date: Dec-2007
Citation: Journal of Economic Dynamics and Control, v. 31, iss. 12, December 2007, p. 3860-3880
Abstract: Financial derivatives commonly contain pre-mature termination clauses, which are embedded rights held by the holder or writer. Well known examples of these stopping rights include the early exercise right in American options, the callable right in callable securities and the prepayment right in mortgage loans. In this paper, we show how to model the mortgagor’s prepayment in mortgage loans and the issuer’s call in the American warrant as an event risk using the intensity based approach, where the propensity of prepayment or calling is modeled by the intensity of a Poisson process. We illustrate that the corresponding pricing formulation resembles the penalty approximation approach commonly used in the solution of the linear complementarity formulation of an optimal stopping problem. We obtain several theoretical results on the prepayment strategies of mortgage loans and calling polices of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem.
Rights: Journal of Economic Dynamics and Control © copyright (2007) Elsevier. The Journal's web site is located at'
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