Pricing Convertible Bonds under the First-Passage Credit Risk Model

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Title:	Pricing Convertible Bonds under the First-Passage Credit Risk Model
Authors:	Dai, Tian-Shyr;Wang, Jr-Yan;Wang, Chuan-Ju;王釧茹
Contributors:	臺北市立大學資訊科學系
Keywords:	Convertible bond;tree;first-passage model
Date:	2014-09
Issue Date:	2019-02-14
Abstract:	A convertible bond is a corporate bond that allows the bond holder to convert the bond into the issuing firm's stock to share the profit and the growth of the firm. Pricing convertible bonds can be intractable due to the hybrid attributes of both fixed-income securities and equities, and their complex relations to the firm's default risk. For pricing methods based on a reduced-form model, the stock price is employed for evaluating the conversion options and the default risk is determined by calibrating the credit spreads of the issuer's straight bonds; however, the relationship among the default probability, the stock price, and the dilution effect (due to bond conversions) are not well analyzed in the reducedform-based methods. In contrast, the relationship among these three factors can be easily analyzed in the structure-form-based pricing methods since these methods directly model the firm's capital structure and the evolution of its value process. However, the firm value cannot be directly observed in the financial markets, and the jump-to-default events are hard to be modeled in these methods. To address the aforementioned issues, this paper proposes a twofactor tree that simultaneously models the issuer's stock price and the short term interest rate processes. In specific, since the stock price can be treated as a contingent claim on the firm's asset, the unobservable firm value and its volatility for each node of the tree can be endogenously derived by taking advantage of the option pricing formula. Then the jump-todefault probability for that node is estimated by taking advantage of “distance to default" measure like Moody's KMV model. In addition, the tree model can also deal with the dilution effect. Numerical results and sensitive analysis are given to confirm the robustness of our pricing method.
Relation:	The 22nd Annual Conference on Pacific Basin Finance, Economics, Accounting, and Management (PBFEAM’14)，Nagoya，2014/09/04~05
Appears in Collections:	[Department of Computer Science] Proceedings

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