Dynkin game for callable-puttable convertible bonds: the valuation and sensitivity analysis

This paper studies the pricing problem for callable-puttable convertible bonds with callput protections and call notice period as a Dynkin game via the backward stochastic differential equation (BSDE) with two reflecting barriers. By virtue of reflected BSDEs, we first reduce such a Dynkin game to an optimal stopping time problem and establish the formulae for the fair price of puttable convertible bond. Based on that, we further obtain the valuation model of callable-puttable convertible bonds and investigate how the call and put clauses affect the value of convertible bonds. In addition, the sensitivity analysis of callable-puttable convertible bonds’ price about some key parameters is considered in virtue of the comparison theorem of doubly reflected BSDEs and is verified by numerical simulations through an obstacle problem for a parabolic partial differential equation.

Keywords

callable-puttable convertible bond, doubly reflected BSDE, Dynkin game, parabolic PDE, sensitivity analysis

2010 Mathematics Subject Classification

35Q91, 49N90, 60H30, 91A80

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K. Du acknowledges the Postdoctoral Innovative Talent Support Program (BX20200199), the National Natural Sciences Foundations of China (No. 11971267, 12001319) and the Natural Science Foundation of Shandong Province (No. ZR2020QA025). Z. Wu acknowledges the Natural Science Foundation of China (No. 11831010, 61961160732), the Natural Science Foundation of Shandong Province (No. ZR2019ZD42) and the Taishan Scholars Climbing Program of Shandong (No. TSPD20210302). D. Zhang acknowledges the Natural Science Foundation of China (No. 11401345).

Received 15 September 2018

Accepted 5 October 2020

Published 5 May 2021