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Dynkin game of convertible bonds and their optimal strategy

Research output: Contribution to journalArticle

Huiwen Yan, Fahuai Yi, Zhou Yang, Gechun Liang

Original languageEnglish
Pages (from-to)64-88
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume426
Issue number1
DOIs
Publication statusPublished - Jun 2015

Documents

  • 1503.08961v1

    1503.08961v1.pdf, 333 KB, application/pdf

    21/07/2015

    Submitted manuscript

    NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

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  • King's College London

Abstract

This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian setting, we investigate the optimal strategy by analyzing the properties of the corresponding free boundary, including its position, asymptotics, monotonicity and regularity. We identify situations when call precedes conversion, and vice versa. Moreover, we show that the irregular payoff results in the possibly non-monotonic conversion boundary. Surprisingly, the price of the convertible bond is not necessarily monotonic in time: it may even increase when time approaches maturity.

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