Callable Barrier Reverse Convertible Securities

Forthcoming, Quantitative Finance, https://doi.org/10.1080/14697688.2021.1912380

28 Pages Posted: 17 Jun 2021

See all articles by Jerome Detemple

Jerome Detemple

Boston University Questrom School of Business; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Yerkin Kitapbayev

North Carolina State University

Date Written: January 19, 2021

Abstract

We study the valuation of callable barrier reverse convertible contracts written on one or two underlying asset prices. We assume the issuer of the contract can call early redemption at any time during a pre-specified time interval. We identify the optimal redemption policy and show, in the single underlying asset case, it is characterized by a time-dependent boundary. The boundary satisfies a nonlinear integral equation of the Volterra type. When there are two underlying assets, the boundary is a surface depending on one price in addition to time. Valuation formulas and associated integral equations are derived. Numerical experiments are performed.

Keywords: Barrier reverse convertible claim, call provision, American put option, geometric Brownian motion, optimal stopping, free-boundary problem, early redemption discount, integral equation

Suggested Citation

Detemple, Jerome and Kitapbayev, Yerkin, Callable Barrier Reverse Convertible Securities (January 19, 2021). Forthcoming, Quantitative Finance, https://doi.org/10.1080/14697688.2021.1912380, Available at SSRN: https://ssrn.com/abstract=3861980 or http://dx.doi.org/10.2139/ssrn.3861980

Jerome Detemple

Boston University Questrom School of Business ( email )

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Boston, MA 02215
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Center for Interuniversity Research and Analysis on Organization (CIRANO)

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Montreal, Quebec H3C 3J7
Canada

Yerkin Kitapbayev (Contact Author)

North Carolina State University ( email )

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Raleigh, NC 27695
United States

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