A parabolic variational inequality arising from the valuation of strike reset options

Zhou Yang, Fahuai Yi, Min Dai

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C smoothness of the free boundary are proven in some situations.

Original languageEnglish
Pages (from-to)481-501
Number of pages21
JournalJournal of Differential Equations
Volume230
Issue number2
DOIs
Publication statusPublished - 15 Nov 2006

Keywords

  • American option
  • Free boundary
  • Option pricing
  • Strike reset option
  • Variational inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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