Pricing Convertible Bonds with Credit Risks and Stochastic Interest Rates

Convertible bonds are one of the essential financial products for corporate finance, while the pricing theory is the key problem to the theoretical research of convertible bonds. This paper demonstrates how to price convertible bonds with call and put provisions using Least-Squares Randomized Quasi-Monte Carlo (LSRQM) method. We consider the financial market with stochastic interest rates and credit risk and present a detailed description on calculating steps of convertible bonds value. The empirical results show that the model fits well the market prices of convertible bonds in China’s market and the LSRQM method is effective.

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PRICING AND HEDGING CONVERTIBLE BONDS: DELAYED CALLS AND UNCERTAIN VOLATILITY

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024906003573 ◽

2006 ◽

Vol 09 (03) ◽

pp. 415-453 ◽

Cited By ~ 7

Author(s):

ALI BORA YIǦITBAŞIOǦLU ◽

CAROL ALEXANDER

Keyword(s):

Interest Rates ◽

Important Determinant ◽

Convertible Bonds ◽

Reduced Form ◽

Hazard Rates ◽

Stochastic Interest Rates ◽

Period Effects ◽

Stochastic Interest ◽

Non Linear ◽

The Common

Arbitrage-free price bounds for convertible bonds are obtained assuming equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior. Uncertainty in volatility is modeled using a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects. Increasingly pessimistic values for the issuer's substitution asset obtain as we introduce more uncertainty during the notice period. Uncertain in volatility, in particular, appears to be an important determinant of the call premium that is so often observed in issuer's call policies.

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Binary Tree Pricing to Convertible Bonds with Credit Risk under Stochastic Interest Rates

Abstract and Applied Analysis ◽

10.1155/2013/270467 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Jianbo Huang ◽

Jian Liu ◽

Yulei Rao

Keyword(s):

Credit Risk ◽

Interest Rates ◽

Stock Prices ◽

Binary Tree ◽

Convertible Bonds ◽

Tree Model ◽

Credit Risks ◽

Derivative Instruments ◽

Stochastic Interest ◽

Financial Derivative

The convertible bonds usually have multiple additional provisions that make their pricing problem more difficult than straight bonds and options. This paper uses the binary tree method to model the finance market. As the underlying stock prices and the interest rates are important to the convertible bonds, we describe their dynamic processes by different binary tree. Moreover, we consider the influence of the credit risks on the convertible bonds that is described by the default rate and the recovery rate; then the two-factor binary tree model involving the credit risk is established. On the basis of the theoretical analysis, we make numerical simulation and get the pricing results when the stock prices are CRR model and the interest rates follow the constant volatility and the time-varying volatility, respectively. This model can be extended to other financial derivative instruments.

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