Warrants bond is one of innovative financial instruments on investment and financing markets in recent years. The traditional approach to model warrants bond is to copy the pricing theory of convertible bond. In this paper, theory is combined with practice in real life to compare the terms and conditions of warrants bond and convertible bond and it is found that there are many differences between those two bonds, including coupon, maturity, exercise price, put and call provisions and credit etc. Therefore, it is necessary to build a more suitable pricing model for warrants bond.
Learning from Tsiveriotis and Fernandes(1998), it is recognized that equity and debt components of warrants bonds are also subject to different default risk and derived a pair of coupled differential equations that can be solved explicitly. Basic value of warrants bond includes two parts, warrant's value and bond's value, where the latter is proved to be equivalent to a risk-free bond minus corresponding quantity put options. Dilution rate when conversing should be the dilution rate of equity ration. Besides, considering the domestic market still exists some investment restrictions currently, warrants bond is valued within the framework of structure models and a new pricing model is established under portfolio constraints in the markets. Based on those, contingent claims are modelled under this market hypothesis, and the assumptions of Black and Scholes(1973) pricing model is relaxed, introducing more realistic factors, studying warrants bond pricing problem under different market conditions in depth.
The pricing of warrants bonds which in unconstrained case is presented. The pricing of warrants bonds and investment portfolios under prohibition of short-selling and borrowing are discussed.
As portfolio constraints obviously exist in reality, it is meaningful to build such a structure model.It shows that the model not only can reflect portfolio constraints in the markets, but also can capture the real-time changes on financial lever of the company very well.
HU Chang-sheng, CHENG Zhi-fu, CHEN Jing, XIONG De-chao
. Pricing Warrants Bonds under Portfolio Constraints[J]. Chinese Journal of Management Science, 2017
, 25(9)
: 11
-18
.
DOI: 10.16381/j.cnki.issn1003-207x.2017.09.002
[1] Tsiveriotis K, Fernandes C. Valuing convertible bonds with credit risk[J]. Journal of Fixed Income,1998,8(2):95-102.
[2] Finnerty J D. Valuing convertible bonds and the option to exchange bonds for stock[R]. Research Paper, Fordham University School of Business,2007.
[3] Constantinides G M. Warrant exercise and bond conversion in competitive markets[J]. Journal of Financial Economics, 1984, 13(3):371-397.
[4] Philips G A. Convertible bond markets[M]. London:Palgrave Macmillan, 1997.
[5] Ferris S P, Jo H, Pinkerton J M, et al.The usage of convertible and warrant bonds by Japanese firms:Risk-shifting or the delayed issuance of equity?[J]. Advances in Financial Economics, 2002, 7(02):185-207.
[6] 刘娥平,史扬.分离债与转债发行条款的比较分析[J].财会通讯(学术版),2007,(11):100-103.
[7] Black F, Scholes M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3):637-654.
[8] Merton R. On the pricing of corporate debt:The risk structure of interest rates[J].Journal of Finance, 1974,29(2):449-470.
[9] Finnerty J D, Emery D R. Options in structured notes:Fix the price or fix the spread?[R].Research Paper, Fordham University Schools of Business, 2014.
[10] Huang Jingzhi,Huang Ming.How much of the Corporate-treasury yield spread is due to credit risk[J]. The Review of Asset Pricing Studies,2012,2(2):153-202.
[11] Karatzas I,Shreve S.Methods of mathematical finance[M].New York:Springer, 2004.
[12] 陈盛业,宋逢明.卖空约束下的公司债券定价[J].运筹与管理,2007,16(2):94-112.
[13] Ingersoll J. An examination of corporate call policies on convertible securities[J]. Journal of Finance, 1977, 32(2):463-478.
[14] Brennam M J, Schwartz E S.Convertible bonds:Valuation and optimal strategies for call and conversion[J].Journal of Finance,1997,17(5):1699-1715.
[15] 杨大楷,杜新乐,刘庆生.浅论我国可转换债券的定价及设计[J]. 中国管理科学, 2001, 9(4):7-15.
[16] Kraft H, Steffensen M. A dynamic programming approach to constrained portfolios[J]. European Journal of Operational Research, 2013, 229(2):453-461.
[17] Fahim A, Huang Y J. Model-independent superhedging under portfolio constraints[J]. Finance and Stochastics, 2016, 20(1):51-81.
[18] 徐枫,胡鞍钢,郭楠.异质信念、卖空限制对证券发行决策的影响[J]. 中国管理科学, 2013, 21(2):1-8.
[19] 方立兵,曾勇.股市收益率高阶矩风险的产生机制检验[J]. 中国管理科学, 2016, 24(4):27-36.
[20] Hong H, Stein J C. Differences of opinion, short-sales constraints, and market crashes[J]. Review of Financial Studies, 2003, 16(2):487-525.
[21] Karatzas I,Kou S G.On the pricing of contingent claims under constraints[J].The Annuals of Applied Probability, 1996, (6):321-369.
[22] Girsanov I V. On transforming a certain class of stochastic processes by absolutely continuous substitution of measures[J]. Theory of Probability & Its Applications, 1960, 5(3):285-301.
[23] Merton R C. Option pricing when the underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1):125-144.
[24] Ronn E I, Verma A K. Pricing risk-adjusted deposit insurance:An option-based model[J]. The Journal of Finance, 1986, 41(4):871-895.