The Valuation and Optimal Policies of Puttable Convertible Bonds

Keywords: Puttable convertible bonds, free boundary problem, jump conditions

Abstract

American-style convertible bonds commonly contain the put provision that allows the investors to put or sell their holdings to the issuer at preset prices and dates. The embedded put option includes a free boundary in addition to the conversion boundary. Because of the correlation of two moving boundaries with the convertible price, the valuation of puttable convertible bonds remains a classical problem in quantitative finance. This paper presents the valuation model of puttable convertible bonds under the Black-Scholes framework. We distinguish between the conventional pricing model and the current work by the realization of a jump in the put price across the hitting time. The jump condition permits the derivation of two recombining differential systems and we explore the impact of jump effect on the pricing dynamic of this innovative financial derivative.

Downloads

Download data is not yet available.

References

Barone-Adesi G., Bermúdez A., & Hatgioannides J. (2003). Two-factor convertible bonds valuation using method of characteristics/finite elements J. Economic Dynamics Control, 27(10), 1801–1831. doi: 10.1016/S0165-1889(02)00083-0

Błach, J., & Łukasik, G. (2017). The role of convertible bonds in the corporate financing: Polish experience. In David Prochazka (Ed.). New Trends in Finance and Accounting (pp. 665–675). Springer Proceedings in Business and Economics. Springer, Cham doi: 10.1007/978-3-319-49559-0_61

Brick, I. E., Palmon, O., & Patro, D. K. (2015). Motivations for issuing puttable debt: An empirical analysis. In Lee C. F., & Lee J. (eds.). Handbook of Financial Econometrics and Statistics (pp. 149–185). New York, NY: Springer. doi: 10.1007/978-1-4614-7750-1_5

Chemmanur, T. J., & Simonyan, K. (2010). What drives the issuance of puttable convertibles: Risk shifting, asymmetric information, or taxes? Financial Management, 39(3), 1027–1068. doi: 10.1111/j.1755-053X.2010.01103.x

Dutordoir, M., Lewis, C., Seward, J., & Veld, C. (2014). What we do and do not know about convertible bond financing. Journal of Corporate Finance, 24, 3–20. doi: 10.1016/j.jcorpfin.2013.10.009

Elkamhi, R., Ericsson, J., & Wang, H. (2012). What risks do corporate bond put features insure against? Journal of Futures Markets, 32(11), 1060–1090. doi: 10.1002/fut.20546

Grimwood, R., & Hodges, S. (2002). The valuation of convertible bonds: A study of alternative pricing models (Warwick Finance Research Institute Working Paper, PP 02–121). Conventry, UK: University of Warwick.

Johnson, P. (2003). Using CFD methods on problems in mathematical finance (Master’s thesis). Manchester: University of Manchester.

McConnell, J. J., & Schwartz, E. S. (1986). LYON taming. The Journal of Finance, 41(3), 561–576. doi: 10.1111/j.1540-6261.1986.tb04516.x

Nyborg, K. G. (2006). The use and pricing of convertible bonds. Applied Mathematical Finance, 3(3), 167–190. doi: 10.1080/13504869600000009

Yang, X., Yu, J., Xu, M., & Fan, W. (2018). Convertible bond pricing with partial integro-differential equation model. Mathematics and Computers in Simulation, 152, 35–50 doi: 10.1016/j.matcom.2018.04.005

Zhu, S. P. & Zhang, J. (2012). How should a convertible bond be decomposed? Decisions in Economics and Finance, 35(2), 113–149. doi: 10.1007/s10203-011-0118-y

Zhu, S. P. (2006) A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield. The ANZIAM Journal, 47(4), 477–494. doi: 10.1017/S1446181100010087

Published
2019-02-28
How to Cite
Adegboyegun, B. (2019). The Valuation and Optimal Policies of Puttable Convertible Bonds. Journal of Finance and Accounting Research, 1(1), 29-33. https://doi.org/10.32350/JFAR.0101.02
Section
Articles