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Callable convertible bonds under liquidity constraints and hybrid priorities

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  • David Hobson
  • Gechun Liang
  • Edward Wang

Abstract

This paper investigates the callable convertible bond problem in the presence of a liquidity constraint modelled by Poisson signals. We assume that neither the bondholder nor the firm has absolute priority when they stop the game simultaneously, but instead, a proportion $m\in[0,1]$ of the bond is converted to the firm's stock and the rest is called by the firm. The paper thus generalizes the special case studied in [Liang and Sun, Dynkin games with Poisson random intervention times, SIAM Journal on Control and Optimization, 57 (2019), 2962-2991] where the bondholder has priority ($m=1$), and presents a complete solution to the callable convertible bond problem with liquidity constraint. The callable convertible bond is an example of a Dynkin game, but falls outside the standard paradigm since the payoffs do not depend in an ordered way upon which agent stops the game. We show how to deal with this non-ordered situation by introducing a new technique which may be of interest in its own right, and then apply it to the bond problem.

Suggested Citation

  • David Hobson & Gechun Liang & Edward Wang, 2021. "Callable convertible bonds under liquidity constraints and hybrid priorities," Papers 2111.02554, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2111.02554
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    References listed on IDEAS

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    1. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Hobson, David, 2021. "The shape of the value function under Poisson optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 229-246.
    4. Huiwen Yan & Zhou Yang & Fahuai Yi & Gechun Liang, 2015. "Dynkin Game of Convertible Bonds and Their Optimal Strategy," Papers 1503.08961, arXiv.org.
    5. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
    6. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    7. Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org, revised Jul 2019.
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