Convertible Bond Valuation with Regime Switching

This chapter introduces the analysis and valuation of bonds with embedded options. For callable bonds, it discusses their unique reinvestment risk and negative convexity. For both callable bonds and puttable bonds, the chapter introduces two additional measures to gauge their risk: yield-to-call and yield-to-put, respectively. The chapter reviews the application of the spot rate curve in bond valuation and introduces the Z-spread to measure bond-specific risk more accurately. To model interest rate risk, the chapter builds a binomial interest rate model and calibrates it with on-the-run Treasury issues. The option-adjusted-spread (OAS) is introduced to measure the bond-specific risk excluding the option effect. The difference between Z-spread and OAS represents the option effect. Common measures of convertible bond risk and value are discussed including the possibility of valuating a convertible bond using option-pricing models and its drawbacks.

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Bond valuation under a discrete‐time regime‐switching term‐structure model and its continuous‐time extension

Managerial Finance ◽

10.1108/03074351111167929 ◽

2011 ◽

Vol 37 (11) ◽

pp. 1025-1047 ◽

Cited By ~ 10

Author(s):

Robert J. Elliott ◽

Tak Kuen Siu ◽

Alex Badescu

Keyword(s):

Term Structure ◽

Discrete Time ◽

Continuous Time ◽

Regime Switching ◽

Structure Model ◽

Term Structure Model ◽

Bond Valuation ◽

Time Regime ◽

Time Extension

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Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

Mathematical Problems in Engineering ◽

10.1155/2014/381943 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Wei-Guo Zhang ◽

Ping-Kang Liao

Keyword(s):

Credit Risk ◽

Regime Switching ◽

Numerical Solutions ◽

Dilution Effect ◽

Convertible Bonds ◽

Bond Pricing ◽

Convertible Bond ◽

Pricing Model ◽

Black Scholes ◽

The Impact

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

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