Corporate bond pricing model with stochastically volatile firm value process

In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation’s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-span of the bond. The volatility of a corporate bond price may have a jump when a credit rating for the bond is changed. Moreover, the volatility of the bond is also assumed to depend on the interest rate. This new model improves the previous existing bond models in which the rating change is only allowed to occur once with an interest-dependent volatility or multi-ratings with constant interest rate. By using a Feynman-Kac formula, we obtain a free boundary problem. Global existence and uniqueness are established when the interest rate follows a Vasicek’s stochastic process. Calibration of the model parameters and some numerical calculations are shown.

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A Simplified Firm Value-Based Risky Discount Bond Pricing Model

Review of Pacific Basin Financial Markets and Policies ◽

10.1142/s0219091507001148 ◽

2007 ◽

Vol 10 (03) ◽

pp. 445-468 ◽

Cited By ~ 3

Author(s):

Alan T. Wang ◽

Sheng-Yung Yang

Keyword(s):

Firm Value ◽

Closed Form Solution ◽

Form Solution ◽

Credit Spread ◽

Bond Pricing ◽

Computational Time ◽

Pricing Model ◽

Management Tools ◽

General Parameter ◽

Parameter Values

This paper proposes a simplified risky discount bond pricing model based on Longstaff and Schwartz (1995). The advantage of this model is that it yields a closed form solution for probability of default. Also, a practical feature with our model is that computing durations and other risk management tools become computationally less expensive, while the appealing properties in the LS model are preserved. The numerical comparisons show that the differences in credit spreads between this model and Longstaff and Schwartz are within a few basis points for fairly general parameter values. Moreover, the computational time is shown remarkably reduced by the simplified model. Sensitivity analysis of credit spread with respect to different parameter values is presented.

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On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate

Quantitative Finance and Economics ◽

10.3934/qfe.2017.3.300 ◽

2017 ◽

Vol 1 (3) ◽

pp. 300-319 ◽

Cited By ~ 6

Author(s):

Jin Liang ◽

◽

Xinfu Chen ◽

Yuan Wu ◽

Hong-Ming Yin ◽

...

Keyword(s):

Interest Rate ◽

Credit Rating ◽

Corporate Bond ◽

Bond Pricing ◽

Stochastic Interest Rate ◽

Pricing Model ◽

Stochastic Interest

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Pricing Corporate Bonds with Credit Risk, Liquidity Risk, and Their Correlation

Discrete Dynamics in Nature and Society ◽

10.1155/2021/6681035 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Xinting Li ◽

Baochen Yang ◽

Yunpeng Su ◽

Yunbi An

Keyword(s):

Financial Crisis ◽

Credit Risk ◽

Liquidity Risk ◽

Market Risk ◽

Risk Tolerance ◽

Corporate Bond ◽

Bond Pricing ◽

Pricing Model ◽

Death Spiral ◽

Trading Model

This paper proposes a generalized bond pricing model, accounting for all the effects of credit risk, liquidity risk, and their correlation. We use an informed trading model to specify the bond liquidity payoff and analyze the sources of liquidity risk. We show that liquidity risk arises from reduced information accuracy and market risk tolerance, and it is market risk tolerance that links credit and liquidity. Then, we extend the traditional bond pricing model with only credit risk by incorporating liquidity risk into the framework in which the probabilities of the two risk events are estimated by a joint distribution. Using numerical examples, we analyze the role of the correlation between credit and liquidity in bond pricing, especially during a financial crisis. We document that the varying correlation between default and illiquidity explains the phenomenon of bond death spiral observed in a financial crisis. Finally, we take the US corporate bond market as an example to demonstrate our conclusions.

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Insider Ownership, Governance Mechanisms, and Corporate Bond Pricing Around the World

Journal of International Money and Finance ◽

10.1016/j.jimonfin.2021.102423 ◽

2021 ◽

pp. 102423

Author(s):

Rob Bauer ◽

Jeroen Derwall ◽

Nora Pankratz

Keyword(s):

Corporate Bond ◽

Bond Pricing ◽

Governance Mechanisms ◽

Insider Ownership ◽

The World

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Do participants in the bond market care about corporate social responsibility? Evidence from China

International Journal of Emerging Markets ◽

10.1108/ijoem-01-2021-0156 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Jun Hu ◽

Wenbin Long ◽

Yu Wang ◽

Linzi Zhou

Keyword(s):

Corporate Social Responsibility ◽

Social Responsibility ◽

Bond Market ◽

Economic Consequences ◽

Corporate Bond ◽

Bond Pricing ◽

Content Type ◽

Market Participants ◽

Risk Environments ◽

Corporate Social

PurposeUsing a sample of listed Chinese companies that issued bonds from 2010 to 2019, the authors empirically test the link between CSR and corporate bond pricing, and the mechanism and channels behind this link.Design/methodology/approachThis study systematically examines whether and how corporate social responsibility (CSR) affects the corporate bond market in China.FindingsFirms with better CSR have higher corporate bond credit ratings and lower corporate bond yield spreads. These associations remain stable in robustness checks, including checks that use regional typhoon disaster as an instrumental variable. The effects of CSR are more significant for firms with a worse information environment and for those operating in high-risk environments. Better CSR is associated with less earnings management, fewer financial restatements and less analyst forecast divergence. In addition, the effects of CSR are more pronounced after the 2013 market-oriented reform and when issuers are non-state-owned enterprises.Practical implicationsBecause market participants can incorporate firms' CSR into their decision-making, establishing an effective channel for communicating CSR between issuers and market participants will enhance the effects of CSR.Social implicationsResearchers need to attend to the mechanisms behind the link between CSR and corporate bond pricing, and to the characteristics of strong environmental contingency in emerging markets, specifically the periods and scenarios in which the effects of CSR change.Originality/valueThis study provides systemic evidence that CSR benefits corporate bond pricing through both informational and reputational channels and that the effects of CSR vary by time and firm. These findings enrich the literatures on both the economic consequences of CSR and the determinants of corporate bond pricing, and provide a plausible explanation for mixed findings on the effects of CSR in previous studies.

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Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance

Open Physics ◽

10.1515/phys-2018-0096 ◽

2018 ◽

Vol 16 (1) ◽

pp. 766-779

Author(s):

Taha Aziz ◽

Aeeman Fatima ◽

Chaudry Masood Khalique

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Heat Equation ◽

Canonical Form ◽

Mathematical Finance ◽

Fundamental Solutions ◽

Bond Pricing ◽

Canonical Forms ◽

Pricing Model ◽

Invariant Approach

AbstractThe invariant approach is employed to solve the Cauchy problem for the bond-pricing partial differential equation (PDE) of mathematical finance. We first briefly review the invariant criteria for a scalar second-order parabolic PDE in two independent variables and then utilize it to reduce the bond-pricing equation to different Lie canonical forms. We show that the invariant approach aids in transforming the bond-pricing equation to the second Lie canonical form and that with a proper parametric selection, the bond-pricing PDE can be converted to the first Lie canonical form which is the classical heat equation. Different cases are deduced for which the original equation reduces to the first and second Lie canonical forms. For each of the cases, we work out the transformations which map the bond-pricing equation into the heat equation and also to the second Lie canonical form. We construct the fundamental solutions for the bond-pricing model via these transformations by utilizing the fundamental solutions of the classical heat equation as well as solution to the second Lie canonical form. Finally, the closed-form analytical solutions of the Cauchy initial value problems for the bond-pricing model with proper choice of terminal conditions are obtained.

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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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