Empirical Evaluation of Hybrid Defaultable Bond Pricing Models

A four‐factor model (the extended model of Schmid and Zagst) is presented for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is an advancement of an earlier three‐factor model. In addition to a firm‐specific credit risk factor, a new systematic risk factor in the form of GDP growth rate is included. This new model is set in the context of other hybrid defaultable bond pricing models and empirically compared to specific representatives. We find that a model based only on firm‐specific variables is unable to capture changes in credit spreads completely. However, it is shown that in this model, market variables such as GDP growth rates, non‐defaultable interest rates and firm‐specific variables together significantly influence credit spread levels and changes.     

基于双因子CIR强度式定价的信用债券投资组合优化

信用风险和利率风险是相互关联影响的。资产组合优化不能将这两种风险单独考虑或简单的相加,应该进行整体的风险控制,不然会造成投资风险的低估。本文的主要工作：一是在强度式定价模型的框架下,分别利用CIR随机利率模型刻画利率风险因素“无风险利率”和信用风险因素“违约强度”的随机动态变化,衡量在两类风险共同影响下信用债券的市场价值,从而构建CRRA型投资效用函数。以CRRA型投资效用函数最大化作为目标函数,同时控制利率和信用两类风险。弥补了现有研究中仅单独考虑信用风险或利率风险、无法对两种风险进行整体控制的弊端。二是将无风险利率作为影响违约强度的一个因子,利用“无风险利率因子”和“纯信用因子”的双因子CIR模型拟合违约强度,考虑了市场利率变化对于债券违约强度的影响,反映两种风险的相关性。使得投资组合模型中既同时考虑了信用风险和利率风险、又考虑了两种风险的交互影响。避免在优化资产组合时忽略两种风险间相关性、可能造成风险低估的问题。     

债券定价及利率风险的市场价格的重构方法

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.     

中国企业债信用风险度量的实证研究

我们基于KMV模型以及Delianedis and Geske(2001)模型,对05国航债进行了信用风险度量分析.根据中国国航在2007年7月23日的收盘价和近三年的财务数据我们对05国航债的信用利差进行了实证分析,并就实证结果提出了自己的观点:由于我国的企业债不是信用债券,而是由国有商业银行担保的债券,因此2007年7月23日05国航债的利差估计值与实际利差的差额547.34个基点应该由担保银行——中国农业银行的信用所消化.     

债券违约是否存在区域传染？——基于中国债券市场融资成本视角

2018年以来中国债券市场违约规模攀升,累计违约金额超2900亿元。债券违约后的负面影响受到投资者、发行人乃至监管部门关注。本文以北京、上海、辽宁等八个辖区为例,选取2016~2019年债券违约及债券发行数据,通过构建违约事件对债券发行价格影响因素模型,分析了债券违约的区域传染效应。研究发现:债券违约引发的信用风险存在区域传染性,主要体现为债券发行前若发行人所属辖区存在违约事件将推升债券融资成本;区域内的传染效应与违约时间距离负相关,当时间距离增长时,传染效应变弱,甚至消失;债券违约风险对不同性质企业的传染效应不同,民营企业受影响尤为显著。     

Thin trading and estimation of systematic risk: An application of an error-correction model

Financial economics literature indicates that estimates for securities' systematic risk, i.e. the beta coefficients, are highly affected by infrequent trading. This is an especially serious problem in small security markets. In this study, the applicability of an error-correction model is investigated for modeling the risk behavior of thinly traded securities. The empirical results from a small stock market, i.e. the Helsinki Stock Exchange, indicate the estimated error-correction term to be highly dependent on the underlying trading frequency of the stock, while the direct effect is dependent merely on the market value of the firm. The model thus appears to produce useful information about the risk characteristics of thinly traded stocks.     

Bayesian corporate bond pricing and credit default swap premium models for deriving default probabilities and recovery rates

This paper develops a Bayesian method by jointly formulating a corporate bond (CB) pricing model and credit default swap (CDS) premium pricing models to estimate the term structure of default probabilities and the recovery rate. These parameters are formulated by incorporating firm characteristics such as industry, credit rating and Balance Sheet/Profit and Loss information. A cross-sectional model valuing all given CB prices and CDS premiums is considered. The quantities derived are regarded as what market participants infer in forming CB prices and CDS premiums. We also develop a statistical significance test procedure without any distributional assumptions for the specified model. An empirical analysis is conducted using Japanese CB and CDS market data.     

On the simulation of portfolios of interest rate and credit risk sensitive securities

We discuss extensions of reduced-form and structural models for pricing credit risky securities to portfolio simulation and valuation. Stochasticity in interest rates and credit spreads is captured via reduced-form models and is incorporated with a default and migration model based on the structural credit risk modelling approach. Calculated prices are consistent with observed prices and the term structure of default-free and defaultable interest rates. Three applications are discussed: (i) study of the inter-temporal price sensitivity of credit bonds and the sensitivity of future portfolio valuation with respect to changes in interest rates, default probabilities, recovery rates and rating migration, (ii) study of the structure of credit risk by investigating the impact of disparate risk factors on portfolio risk, and (iii) tracking of corporate bond indices via simulation and optimisation models. In particular, we study the effect of uncertainty in credit spreads and interest rates on the overall risk of a credit portfolio, a topic that has been recently discussed by Kiesel et al. [The structure of credit risk: spread volatility and ratings transitions. Technical report, Bank of England, ISSN 1268-5562, 2001], but has been otherwise mostly neglected. We find that spread risk and interest rate risk are important factors that do not diversify away in a large portfolio context, especially when high-quality instruments are considered.     

Asset liability management for open pension schemes using multistage stochastic programming under Solvency-II-based regulatory constraints

Open private pension schemes are subject to risk-based regulation. In this context, asset and liability management (ALM) frameworks for pension plan operators are increasingly based on multistage stochastic programming (MSP). The significant advances in MSP modeling notwithstanding, previous works ignore risk-based regulatory constraints such as those in the Solvency II Directive. In this work, we propose an ALM model for open pension schemes based on an MSP model with a thorough representation of a risk-based regulation. Our proposal aims to define a dynamic optimal asset allocation including a detailed depiction of bond coupon payments, based on insolvency risk measures over a planning horizon. We present a realistic case study based on the Brazilian market, where the regulator imposes Solvency-II-compatible constraints on credit, underwriting, and operational risks. We develop a computationally tractable MSP model with explicit regulatory constraints, which induce risk aversion for even risk-neutral open pension plan operators.     

Valuation and risk assessment of participating life insurance in the presence of credit risk

In participating life insurance, management decisions regarding the asset composition can substantially impact the value of a policy from the policyholders’ perspective as well as the insurer’s risk situation. Due to the long-term guarantees often embedded in these contracts, life insurers typically invest a considerable portion of their capital in long-term assets such as corporate and government bonds. Besides interest rate risk, the value of these bond investments is thus particularly influenced by credit risk. Thus, the aim of this paper is to examine the impact of market risk associated with the asset composition on fair valuation and risk assessment with focus on credit risk and its interaction with equity risk and interest rate risk. Our analysis emphasizes that the consideration of credit risk associated with bonds has a strong impact on the fair valuation and risk measurement in the context of participating life insurance contracts, even in case of higher grade bond exposures.     

Credit spreads, endogenous bankruptcy and liquidity risk

In this paper, we consider a bond valuation model with both credit risk and liquidity risk to show that credit spreads are not negligible for short maturities. We adopt the structural approach to model credit risk, where the default triggering barrier is determined endogenously by maximizing equity value. As for liquidity risk, we assume that bondholders may encounter liquidity shocks during the lifetime of corporate bonds, and have to sell the bond immediately at the price, which is assumed to be a fraction of the price in a perfectly liquid market. Under this framework, we derive explicit expressions for corporate bond, firm value and bankruptcy trigger. Finally, numerical illustrations are presented.     

考虑公司信息披露情绪的欧式脆弱期权定价

从公司信息披露的角度来看,定量数据直观地反映了公司的经营和财务状况,而描述性的非结构文本信息是对定量数据的有效补充。本文从公司年报中挖掘信用违约文本信息,构建语调变量情绪指标,以调控脆弱期权的违约临界值,改进经典的Klein欧式脆弱期权定价模型。研究表明:随着语调变量指标的增大,欧式看涨看跌期权价格呈递减趋势,且指标越接近1,期权价格递减速度越快,说明期权价格对负向情绪更加敏感,符合金融市场实际情况。此外,应用研究发现不考虑情绪指标的Klein模型倾向于低估期权价格,考虑公司信息披露情绪的脆弱期权定价模型能更准确地分析财务困境对信用风险的影响,结果更贴近实际情况。     

基于担保的中小企业融资的集合票据的定价研究

在简约化模型框架下,考虑担保机构的违约对集合发债融资的中小企业有违约传染的影响,通过引进一个几何双曲线衰减函数,得到了集合票据的定价公式,在此基础上对担保集合票据所隐含的信用风险进行分析.结果表明:担保机构的存在能显著降低集合票据的信用利差,提高其市场发行价格;且有担保下,担保机构的违约传染风险因子越大,相应的集合票据价格就越低,违约概率越大,信用利差越高,担保价值越低.     

Does the financial market compensate investors for operational Losses?

It is well known that several industries, like the hotel industry, are subject to low frequency high impact events resulting from their operations. However, there is a dearth of academic research in this area. In this paper we propose an innovative methodology to study the problem using a combination of Asset Pricing Models and an original database. We find that asset prices compensate investors not only for market and credit risk, but also for operational risk.     

地方政府债券信用风险缓释工具定价研究

随着地方政府债券发行规模的扩大,地方政府债务的信用风险日益凸出。本研究以企业债信用风险缓释工具的推出为契机,借鉴结构化模型的思路和KMV模型求解违约概率的逻辑,通过Monte Carlo方法模拟地方政府的违约过程,直接测算地方政府的整体违约概率;结合简约化模型的思路测算地方政府债券的具体违约概率,计算信用风险缓释工具的理论价格,从而构建了地方政府债券信用风险缓释工具的混合定价模型。研究发现,以企业债券为标的测算出的模型理论价格与市场报价基本一致,参数的敏感性检验进一步验证了模型的理论自洽性和实证可靠性。上述结论或将为新《预算法》实施过程中地方政府债务的治理与掌控及中国区域性、系统性金融风险的防范提供新思路。     

A multinomial tree model for pricing credit default swap options

Among the traded credit derivatives, the market interest in credit default swap options (CDSwaptions) is enormous. We propose a multinomial tree model to price Bermudan CDSwaptions. Our basic rationale is that we distribute the occurring probability for each node in a branch proportional to the probability density function of the assumed (normal) distribution. Through this approach, without the need of solving a large number of equations simultaneously, only the first four moments are required to build an arbitrarily large N-branches tree. We also demonstrate the detailed model implementation procedure including the valuation and the estimation of critical prices through an empirical example in Tucker and Wei (J Fixed Income 15(1):88–95, 2005). Numerical results show that, in the valuation, the proposed multinomial tree model is accurate and can significantly save pricing time under the same degree of accuracy as the binomial tree model. In the estimation of critical prices, the results are less accurate than those in the valuation, but the relative errors are acceptable.     

Risk factor analysis and portfolio immunization in the corporate bond market

In this paper we develop a multi-factor model for the yields of corporate bonds. The model allows the analysis of factors which influence the changes in the term structure of corporate bonds. More than 98% of the variability in the corporate bond market is captured by the model, which is then used to develop credit risk immunization strategies for corporate bonds of multiple credit ratings. Empirical results are given for the US market using data for the period 1992–1999.     

Securitization, structuring and pricing of longevity risk

Pricing and risk management for longevity risk have increasingly become major challenges for life insurers and pension funds around the world. Risk transfer to financial markets, with their major capacity for efficient risk pooling, is an area of significant development for a successful longevity product market. The structuring and pricing of longevity risk using modern securitization methods, common in financial markets, have yet to be successfully implemented for longevity risk management. There are many issues that remain unresolved for ensuring the successful development of a longevity risk market. This paper considers the securitization of longevity risk focusing on the structuring and pricing of a longevity bond using techniques developed for the financial markets, particularly for mortgages and credit risk. A model based on Australian mortality data and calibrated to insurance risk linked market data is used to assess the structure and market consistent pricing of a longevity bond. Age dependence in the securitized risks is shown to be a critical factor in structuring and pricing longevity linked securitizations.     

中国利率风险溢酬:时变特征与影响因素

利率风险溢酬是长期利率的组成部分,解读它所包含的信息、寻找它的来源有着重要的经济意义。本文先使用利率仿射模型,计算出先验的中国国债利率期限溢酬,然后构建VECM模型,运用脉冲响应、方差分析等技术,分析国债利率的风险溢酬和主要宏观经济变量的动态关系,发现宏观变量对溢酬的影响在当期和滞后几期有明显差异,CPI和GDP是影响最大的两个因素,但信贷供应量和M1的作用也较大。我们同时也发现银行间市场投资者比交易所市场投资者更易受到宏观经济的影响。     

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.