投资组合约束下分离交易可转债的定价

Pricing Warrants Bonds under Portfolio Constraints

分离债是近十年来在投融资领域中的创新金融工具之一,本文试图从结构化模型角度对这一产品进行定价。通过引入市场限制条件并加以刻画,建立新的分离债定价模型。具体而言,先参照Tsiveriotis和Fernandes(1998)等的思路将分离债拆分为权证和债券两部分,再借鉴Karatzas和Kou(1996)和Karatzas和Shreve(2004)的方法分别推导两者在投资组合约束下的无套利价格上界和下界,进而得出分离债的无套利价格区间。由于投资组合约束在现实市场中普遍存在,因此建立这种结构化模型是具有实际意义的。该模型不仅能反映现实市场对投资组合的约束,还可以捕捉到公司杠杆的实时变化。

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,studyingwarrants 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.