Pricing credit-risky bonds using recovery rate uncertainty and macro-regime switching

Abstract

A proposed model is used to account for both the recovery rate and regime-switching uncertainties for pricing credit-risky bonds. A two-factor hazard rate model (TFHRM) is also considered, where the dynamics of both instantaneous forward rates and asset values are modeled using Markov-modulated geometric Brownian motions (MMGBMs). Moreover, a macroeconomic factor is incorporated into the MMGBMs. The model complexity is resolved through the introduction of an endogenous intensity function and a recovery rate under the TFHRM. A semi-closed-form solution for pricing defaultable bonds is derived along with a pricing formula for credit spread. A credit cycle is constructed to reflect changes in industry characteristics and macroeconomic factors. The empirical study demonstrates that the inclusion of a stochastic recovery rate increases the model’s pricing accuracy, and the results indicate a close interaction among business cycles, recovery rates, and credit ratings.

KEYWORDS:

• Credit-risky bond
• stochastic recovery rate
• credit cycle
• a two-factor hazard rate model
• regime-switching

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Refer to Chen, Hsu, and Li (2016) for details of the numéraire change.

2 The proof of Equation (5) and the representation of ${\theta }_{\varphi }\left(t\right)$ refer Appendix 2.

3 The proof of Equation (8) refers Appendix 3.

4 The derivation is available upon request from the authors.

5 The credit ratings are divided into three rating groups from highest to the lowest as follows: high (Aaa–A1), medium (Baa2), and low (Ba1). Anadarko Petroleum Corporation (APC) credit rating: Ba2; American Telephone and Telegraph Company (ATT) credit rating: Baa2; Occidental Petroleum Corporation (OXY) credit rating: Ba1; Fannie Mae (FAMN) credit rating: Aaa; and JPMorgan Chase (JPM) credit rating: A2.

6 The model parameters are calibration as follows: $\text{SSE}=\underset{\mathbf{\Theta }}{min}\sum _t{(\stackrel{\sim }{\text{CRB}\left(t\right)}-\text{CRB}(t\left)\right)}^2,$where the set $\mathbf{\Theta }$ denotes a set of parameters, and the market and the theoretical prices are denoted by $\text{CRB}(t{)}^{\sim }$ and $\text{CRB}\left(t\right)$. SSE represents sum of error square.

7 The derivation is available upon request from the authors.

Additional information

Notes on contributors

Son-Nan Chen

Son-Nan Chen is currently a Professor of Finance at Shanghai Advanced Institute of Finance (SAIF), Shanghai Jiao Tong University. Before joining SAIF, he was Chairman and Chair Professor of Finance and Director of Research Center on Financial Engineering in National Chengchi University (Taiwan). Before returning to Asia, Professor Chen was a tenured Professor of Finance at the University of Maryland, College Park. Professor Chen's research focuses on options, futures and derivatives products, investment analysis and portfolio theory, international finance, corporate finance, capital market theory, statistics and econometrics. He has published a good number of research papers in top academic journals, such as Journal of Finance, Journal of Financial and quantitative Analysis (JFQA), Management Science, Journal of Futures Markets, Journal of Derivatives, Insurance: Mathematics and Economics, Quantitative Finance, European Journal of Finance, etc. He has acted as editors for journals like Advances in Investment Analysis, Portfolio Management and Global Finance Journal, etc. Professor Chen also serves on professional associations, such as American Finance Association and Financial Management Association. Professor Chen offers courses “Financial Engineering”, “Risk Management”, “Derivative Securities”, “Structured Product Design and Innovation (SPDI): Case Study”, and “Alternative Investments and Hedge Fund Strategies” at SAIF. He has also published more than ten books on options, Financial Engineering, Fixed-income Securities, Structured Products Design and Innovation, Credit Risk Derivatives, Risk Management, etc. Professor Chen holds a Ph.D. in Financial Economics, Mathematical Statistics and Econometrics (1976) from University of Georgia.

Pao-Peng Hsu

Pao-Peng Hsu is an associate Professor of Department of Insurance and Finance Management at Chaoyang University of Technology. She holds a Ph.D. in Money and Banking from National Chengchi University, Taiwan. Her research focuses on options, futures and credit derivatives products and fixed income.

Kuo-Yuan Liang

Kuo-Yuan Liang is a director at Yuanta Bank and the retired founder of the Yuanta-Polaris Research Institute in Taipei. He has a PhD in economics from Duke University. Before working in the financial industry, he held a professorship in Economics at National Tsing Hua University (Hsin-Chu, Taiwan), and National Taiwan University. In 2010, he was awarded an honorary professor in the College of Technology Management by National Tsing Hua University. His expertise centers on forecasting, econometrics, macroeconomics, and finance.