Intensity-based framework and penalty formulation of optimal stopping problems

Min Dai, Yue Kuen Kwok, Hong You

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

Financial derivatives commonly contain premature 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 policies of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem.

Original languageEnglish
Pages (from-to)3860-3880
Number of pages21
JournalJournal of Economic Dynamics and Control
Volume31
Issue number12
DOIs
Publication statusPublished - Dec 2007
Externally publishedYes

Keywords

  • Callable feature
  • Event risk
  • Intensity approach
  • Linear complementarity formulation
  • Mortgage prepayment
  • Penalty method

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics

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