On a multiple credit rating migration model with stochastic interest rate

In this paper, we explore a pricing model for corporate bond accompanied with multiple credit rating migration risk and stochastic interest rate. The bond price volatility strongly depends on potentially multiple credit rating migration and stochastic change of interest rate. A free boundary problem of partial differential equation is presented, which is the equivalent transformation of the pricing model. The existence, uniqueness, and regularity for the free boundary problem are established to guarantee the rationality of the pricing model. Due to the stochastic change of interest rate, the discontinuous coefficient in the free boundary problem depends explicitly on the time variable but is convergent as time tends to infinity. Accordingly, an auxiliary free boundary problem is constructed, whose coefficient is the convergent limit of the coefficient in the original free boundary problem. With some constraint on the risk discount rate satisfied, we prove that a unique traveling wave exists in the auxiliary free boundary problem. The inductive method is adopted to fit the multiplicity of credit rating. Then we show that the solution of the original free boundary problem converges to the traveling wave in the auxiliary free boundary problem. Returning to the pricing model with multiple credit rating migration and stochastic interest rate, we conclude that the bond price profile can be captured by a traveling wave pattern coupling with a guaranteed bond price with face value equal to one at the maturity.     

Liquidity and credit risk

The paper uses fuzzy measure theory to represent liquidity risk, i.e. the case in which the probability measure used to price contingent claims is not known precisely. This theory enables one to account for different values of long and short positions. Liquidity risk is introduced by representing the upper and lower bound of the price of the contingent claim computed as the upper and lower Choquet integral with respect to a subadditive function. The use of a specific class of fuzzy measures, known as g λ measures enables one to easily extend the available asset pricing models to the case of illiquid markets. As the technique is particularly useful in corporate claims evaluation, a fuzzified version of Merton's model of credit risk is presented. Sensitivity analysis shows that both the level and the range (the difference between upper and lower bounds) of credit spreads are positively related to the ‘quasi debt to firm value ratio’ and to the volatility of the firm value. This finding may be read as correlation between credit risk and liquidity risk, a result which is particularly useful in concrete risk-management applications. The model is calibrated on investment grade credit spreads, and it is shown that this approach is able to reconcile the observed credit spreads with risk premia consistent with observed default rate. Default probability ranges, rather than point estimates, seem to play a major role in the determination of credit spreads.     

信贷人存货质押贷款中最优质物甄别合同研究

存货抵押贷款中,信用风险主要来源于抵押物价格和流动性风险,信贷人确定适当的利率和贷款价值比能够有效缓释信用风险。对于已知抵押物价格风险和流动性风险,以信贷市场结构作为约束条件,求解出使信贷人期望利率收益最大化合同利率和贷款价值比。当抵押物流动性风险增加时,信贷人最优贷款合同应该是名义利率和贷款价值比均下降;对于抵押物价格波动满足正态分布的情况,若抵押物价格风险增大,信贷人最优贷款合同应该是名义利率和贷款价值比均上升。数值算例的结果基本验证了以上结论,并与现实情况相接近。     

在约化模型下具有随机回收率的公司债券定价

在假设违约过程和利率过程相关的情形下,利用无套利原理构造了具有随机回收率的公司债券定价模型,然后运用偏微分方程方法给出了公司债券的价格表达式,最后讨论了模型中的参数对信用利差的影响.     

双跳-扩散过程下的脆弱期权定价

本文考虑含有交易对手违约风险的衍生产品的定价,以公司价值信用风险模型为基础,在标的资产价格和公司价值均服从跳-扩散过程的情况下,运用结构化的方法对脆弱期权定价进行建模,建立了双跳-扩散过程下的脆弱期权定价模型,分别在公司负债固定和随机的情况下推导出了脆弱期权的定价公式.     

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.     

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.     

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。     

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。     

Utility indifference valuation of corporate bond with rating migration risk

A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a multi-rating bond and obtain closed formulae in a three-rating case. Based on the pricing formulae, the impacts of the parameters on the indifference price are analyzed and some reasonable financial explanations are provided as well.     

The challenge in managing new financial risks: adopting an heuristic or theoretical approach

The financial crisis began with the collapse of Lehman Brothers and the subprime asset backed securities debacle. Credit risk was turned into liquidity risk, resulting in a lack of confidence among financial institutions. In this article, we will propose a way to model liquidity risk and the credit risk in best practices. We will show that liquidity risk is a new type of risk and the current way to deal with it is based solely on observed variables without any theoretical link. We propose an heuristic approach to combine the numerous liquidity risk indicators with a logistic regression for the first time. In regards to credit risk, several articles prove that the best practice is to use an option model to appreciate this risk. We will present our methodology using stochastic diffusion for the interest rate because currently the yield curves aren’t liquid. This approach is more relevant because the basis model in prior publications has a constant interest rate or a forward rate. Both models allow a better understanding of liquidity and credit risks and the further development of research deals with the link between these two financial risks.     

企业债券组合的优化问题研究

信用风险已成为金融业面临的最重要风险形式.通过结构模型估计企业债券的未来价格,建立了投资损失函数,并利用CV aR风险度量方法构造了期望收益最大化的债券组合优化模型,最后利用我国债券市场数据进行了实证分析.     

A Bond Pricing Model with Credit Migration Risk: Different Upgrade and Downgrade Thresholds

Acta Mathematicae Applicatae Sinica, English Series - In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising...     

成也萧何,败也萧何？——高管金融经历与公司债券融资

基于印记理论和高层梯队理论,本文以2008至2018年发行公司债券的上市公司为研究对象,考察高管金融经历对公司债券融资的影响机理。结果表明:首先,高管金融经历在提高公司债券发行成功率的同时也会增加债券融资成本和违约风险,而对发债规模与期限并不会产生显著影响,在控制可能的内生性问题后结论依然成立;其次,具有金融经历的高管所任职公司会通过盈余管理来提高债券发行成功率,但也会增加债券的融资成本和违约风险;最后,具有证券公司或商业银行工作经历的高管对公司债券融资的影响更为显著。本文有助于实务界和理论界理解高管异质性特征对公司债券融资的影响机制,为监管部门制定防范金融风险的政策提供可靠的理论依据。     

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.     

Evaluating corporate bonds with complicated liability structures and bond provisions

This paper presents a general and numerically accurate lattice methodology to price risky corporate bonds. It can handle complex default boundaries, discrete payments, various asset sales assumptions, and early redemption provisions for which closed-form solutions are unavailable. Furthermore, it can price a portfolio of bonds that accounts for their complex interaction, whereas traditional approaches can only price each bond individually or a small portfolio of highly simplistic bonds. Because of the generality and accuracy of our method, it is used to investigate how credit spreads are influenced by the bond provisions and the change in a firm’s liability structure due to bond repayments.     

Monte Carlo analysis of convertible bonds with reset clauses

This paper analyzes some features of non-callable convertible bonds with reset clauses via both analytic and Monte Carlo simulation approaches. Assume that the underlying stock receives no dividends and that it has credit risk of the issuer. We mean by reset that the conversion price is adjusted downwards if the underlying stock price does not exceed pre-specified prices. Reset convertibles are usually issued when the outlook for the issuer is unfavorable. The price of any convertible bonds can be approximately viewed as a sum of values of an otherwise identical non-convertible bond plus an embedded option to convert the bond into the underlying stock. In this paper, we first develop an exact formula for the conversion option value of the European riskless convertible in the classical Black–Scholes–Merton framework. It is shown by Monte Carlo simulation that conversion option value estimates of the American risky convertible are located in a certain region defined by this formula. From estimates of the conversion probability, it is also shown that there exists an optimal reset time in the latter half of the trading interval.     

违约强度由Lévy从属过程驱动的约化信用风险模型及信用违约互换的定价

本文引入一个约化信用风险模型,其中违约强度定义为从属过程,即非负增Lévy过程.用概率方法得到了违约时间分布的解析表达式.利用该解析表达式,给出了该信用风险模型下的信用违约互换(Credit Default Swaps)的闭形式的定价公式.     

标准存货质押融资业务贷款价值比率研究

确定合适的质押存货贷款价值比率能够使银行有效地缓释存货质押融资业务的信用风险。沿着简化式的思路，本文综合考虑了外生的企业违约概率，质押存货的价格波动率，贷款的周期和盯市频率等因素的影响，为银行在保持风险容忍水平一致的情况下确定特定存货质押融资业务的相应贷款价值比率提供了一个基本模型。此外，针对存货质押融资的现状，本文还将清算延迟、流动性风险和非零的触发水平等情况引入基本模型中进行了拓展研究。     

基于信用利差与Logistic回归的公司违约概率测算模型与实证研究

用Logistic模型计算公司违约概率在实际应用中存在两个问题:一是在缺乏公司违约记录数据库或违约记录数据库不典型的情况下,无法应用该模型或模型计算结果不准确;二是现有Logistic违约概率模型忽视了不同行业财务指标分布特征的差异性,导致公司违约概率计算结果的准确性降低。针对问题一,本文通过公司债券信用利差计算市场隐含的公司违约概率,在Logistic变换的基础上进一步确定Logistic线性回归的参数,使得公司违约概率的计算结果符合债券市场的实际状况。针对问题二,通过不同行业关键财务指标的单因子方差分析,证实了行业间财务指标的分布特征具有显著性差异,通过拟合优度证实了区分行业建立Logistic违约概率模型可显著提高违约概率测算的准确性。本文Logistic违约概率模型的构建过程如下:通过初选财务指标的相关性分析,删除反映信息重复的财务指标;通过Logistic回归中财务指标系数的显著性检验,删除对违约概率解释能力弱的财务指标;以Logistic回归的拟合优度为标准,选取各样本行业Logistic违约概率模型的关键财务指标,建立了机械设备等5个样本行业的Logistic违约概率模型,为样本内行业公司违约概率的准确测算提供模型与方法。本文的创新与特色:一是在无套利条件下,通过公司债券信用利差计算市场隐含的公司违约概率,并对其进行Logistic变换,作为Logistic线性回归的被解释变量,解决了在缺乏公司违约记录数据情况下Logistic违约概率模型的参数估计问题;二是通过单因子方差分析方法,证实了行业间财务指标的分布特征具有显著性差异,说明应区分行业建立Logistic违约概率模型;三是通过财务指标间的相关分析删除反映信息重复的财务指标,通过财务指标系数的显著性检验删除对公司违约概率解释能力弱的财务指标,保证了Logistic违约概率模型中关键财务指标选取的合理性;四是实证研究结果表明,不同行业的Logistic违约概率模型的关键财务指标不同,同一财务指标的参数也存在显著差异。实证研究结果还表明,区分行业建立Logistic违约概率模型与不区分行业相比,前者可将拟合优度及调整后的拟合优度提高近1倍。本文研究结果对于提高公司违约概率测算的准确性具有重要参考意义,对于商业银行贷款定价、公司债券发行定价、银行信用风险管理具有重要参考意义。