Valuation of a Credit Swap of the Basket Type

This article provides a simple model to value a credit swap ofthe basket type. Unlike the previous literature, we considerthe joint survival probability of occurrence times of creditevents in terms of stochastic intensity processes under the assumptionof conditional independence. Based on the joint survival probability,such a credit swap can be valued under the risk-neutral valuationframework. Assuming that the default intensity processes followthe extended Vasicek model with a correlation structure, an analyticexpression of the valuation formula is derived. Some numericalexample is given to demonstrate the usefulness of our model.     

Modeling of Contagious Credit Events and Risk Analysis of Credit Portfolios

We present a new model of the occurence of credit events such as rating changes and defaults for risk analyses of some portfolio credit derivatives. The framework of our model is based on a so-called top-down approach. Specifically, we first consider modeling the point process of each type of credit event in the whole economy using a self-exciting intensity process. Next, we characterize the point processes of credit events in the underlying sub-portfolio using random thinning processes specified by the distribution of credit ratings in the sub-portfolio. One of the main features of our model is that the model can capture credit risk contagion simultaneously among several credit portfolios. We present a credit event simulation algorithm based on our model and illustrate an application of the model to risk analyses of loan portfolios.     

Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model

We present a methodology for valuing portfolio credit derivatives under a reduced form model for which the default intensity processes of risk assets follow the one-factor Vasicek model. A closed-form solution of joint survival time distribution is obtained. The solution is applied to value credit derivatives of a credit default swap index and collateralized debt obligation. The limitation of methods using the Vasicek model is discussed. We propose that the method is valid and efficient for a portfolio with small-scale correlated risk assets, for which the acceptable size is much greater than for the traditional method. Numerical examples and parameter analysis are also presented.     

Optimal retention levels,given the joint survival of cedent and reinsurer

A certain volume of risks is insured and there is a reinsurance contract, according to which claims and total premium income are shared between a direct insurer and a reinsurer in such a way, that the finite horizon probability of their joint survival is maximized. An explicit expression for the latter probability, under an excess of loss (XL) treaty is derived, using the improved version of the Ignatov and Kaishev's ruin probability formula (see Ignatov, Kaishev & Krachunov. 2001a) and assuming, Poisson claim arrivals, any discrete joint distribution of the claims, and any increasing real premium income function. An explicit expression for the probability of survival of the cedent only, under an XL contract is also derived and used to determine the probability of survival of the reinsurer, given survival of the cedent. The absolute value of the difference between the probability of survival of the cedent and the probability of survival of the reinsurer, given survival of the cedent is used for the choice of optimal retention level. We derive formulae for the expected profit of the cedent and of the reinsurer, given their joint survival up to the finite time horizon. We illustrate how optimal retention levels can be set, using an optimality criterion based on the expected profit formulae. The quota share contract is also considered under the same model. It is shown that the probability of joint survival of the cedent and the reinsurer coincides with the probability of survival of solely the insurer. Extensive, numerical comparisons, illustrating the performance of the proposed reinsurance optimality criteria are presented.     

Catastrophic Default and Credit Risk for Lending Institutions

Mortgage insurance does insure lenders against most ordinary default: that default induced by price movements in the overall housing market. However, private mortgage insurance typically excludes coverage of the truly catastrophic default resulting from such acts of God as fire, floods, earthquakes, and hurricanes, increasingly familiar in the United States in recent years. Often, these events affect a substantial portion of the houses within a particular neighborhood or region; and if disaster insurance or government aid is inadequate or nonexistent, the default is likely to occur, putting the credit institution at risk. This paper uses a two-state option model with an added jump process that accounts for the possibility and severity of a catastrophe. The paper then uses that information to determine the credit risk to a lender. In addition, this article goes beyond the standard market valuations typical of an option model in reporting the distribution of events that average up to the market cost of the lenders liability. This involves doing probability calculations not present in the usual valuation determinations of option pricing. The point of this article is that the option-pricing methodology provides the means for calculating such probability distributions, thus improving credit risk evaluations for the lender.     

Pricing Sovereign Credit Risk of Poland: Evidence from the CDS Market

We analyze the market assessment of sovereign credit risk using a reduced-form model to price the credit default swap (CDS) spreads, thus enabling us to derive values for the probability of default (PD) and loss given default (LGD) from the quotes of sovereign CDS contracts. We compare different specifications of the models allowing for both fixed and time-varying LGD, and we use these values to analyze the sovereign credit risk of Polish debt throughout the period of a global financial crisis. Our results suggest the presence of a low LGD and a relatively high PD during a recent financial crisis.     

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

中小企业集合债券总体信用风险度量研究

中小企业集合债券总体信用风险既包括系统风险产生的周期性违约风险,又包括相互关联关系导致的传染性违约风险。首先通过对因素模型的改进构建模型Ⅰ,研究集合债券的周期性违约风险;在此基础上引入违约传染建立模型Ⅱ,分析违约传染对违约概率及违约相关性的影响,研究集合债券的总体信用风险。最后基于模型Ⅱ进行算例研究,得出结论：企业间的相互关联关系降低了其1次违约概率,增加了其多次违约概率即违约相关性。     

Credit rating dynamics and Markov mixture models

Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence, we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm’s ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical current credit ratings can have substantially different transition probability vectors. We also find that conditioning on the state of the business cycle or industry group does not remove the heterogeneity with respect to the rate of movement. We go on to compare the performance of mixture and Markov chain using out-of-sample predictions.     

信用风险缓释工具定价研究

通过对信用风险缓释工具定价进行研究得出:(1)CRM定价的主要影响因素包括无风险基准利率,标的债券的风险敞口、违约概率、违约损失率和期限,以及CRM期限等。(2)同期国债利率和央行票据利率作为CRM的基准利率较为恰当,且模型定价对不同期限、不同信用等级的CRM定价区分度较为合理,模型定价与CRM发行交易定价较为接近,适合我国现阶段CRM产品定价。(3)可以从完善CRM定价基础数据库、探索CRM定价无风险基础利率、创新CRM标的债券评级制度、引导CRM市场主体多元化和优化CRM市场做市商制度等方面提出CRM定价优化对策。     

基于Logistic模型的单个信用资产违约概率预测

在信用风险管理领域,由于中国商业银行信贷数据只满足Logistic模型的要求,因而预测单个信用资产违约率只能以Logistic模型为主线建模。以中国某商业银行1999~2005年的信贷数据为样本,实证分析得出,企业本身、宏观经济、地区及行业四方面因素对企业违约概率存在显著相关性。通过以上述四因素为变量,所构建的预测电力、公路、城镇建设三个行业信用资产违约概率的Logistic模型分析与预测单个信用资产违约的结果来看,四要素模型对中国商业银行的信用风险管理具有参照价值。     

Credit rating dynamics in the presence of unknown structural breaks

In many credit risk and pricing applications, credit transition matrix is modeled by a constant transition probability or generator matrix for Markov processes. Based on empirical evidence, we model rating transition processes as piecewise homogeneous Markov chains with unobserved structural breaks. The proposed model provides explicit formulas for the posterior distribution of the time-varying rating transition generator matrices, the probability of structural break at each period and prediction of transition matrices in the presence of possible structural breaks. Estimating the model by credit rating history, we show that the structural break in rating transitions can be captured by the proposed model. We also show that structural breaks in rating dynamics are different for different industries. We then compare the prediction performance of the proposed and time-homogeneous Markov chain models.     

Capital Allocation for Portfolio Credit Risk

Capital allocation rules are derived that maximize leverage while maintaining a target solvency rate for credit portfolios where risk is driven by a single common factor and idiosyncratic risk is fully diversified. Equilibrium conditions ensure that capital allocations depend on interest earnings as well as credits’ probability of default, endogenous loss given default, and asset correlation. Capitalization rates exceed those estimated using Gaussian credit loss models. Results demonstrate that credit risk is undercapitalized by the Basel II AIRB approach in part because of ambiguities regarding the definition of loss given default. An alternative proposed capital rule removes this bias.     

信用缺失环境下的农户信用评估指标体系构建研究

通过调查某信用社713个农户的贷款记录,运用层次分析法(AHP)设计一套农户信用评估指标体系,通过层次单排序和层次综合排序确定各个因素层指标的权重,然后,选取权重值较大的9个指标作为神经网络模型(ANN)的输入层,利用AHP-ANN组合模型,最终得到农户的信用等级和信用评分。实证研究结果表明,这是一种信用缺失环境下进行农户信用评估的有效方法。     

Additional Credit for Liquidity-Constrained Individuals: High-Interest Consumer Credit in Korea

We find that the delinquency probability on formal sector debts of private loan borrowers in Korea increases from 2.4% to 20% in the first year after the borrowing and to 32% in the second year. This increase happens despite private loan borrowers trying to rebuild their financial health by reducing formal sector debts, credit card cash service balances, and credit card purchases during the post-borrowing period. This limits the possibility of moral hazard driving the results. Private loan amounts are positively associated with the delinquency probability after controlling other commonly used variables, suggesting that they contain additional information on the worsening financial situation of an individual.     

Implied Default Probability and Credit Derivatives

Recently many kinds of credit derivatives are traded in the market. The default probability implied in the market becomes important to price some credit derivatives. Also it is useful for managing the credit risk because it includes the market information. In this paper we show how to calculate the implied default probability in the default swap market or the defaultable bond market.This paper is developed from author’s master thesis (Matsumoto, 2000), Graduate School of Systems Management, the University of Tsukuba.     

融资约束下的农户信贷需求及其缺口研究

本文基于需求引导的分析范式,以四川省巴中为例,对融资约束下的农户信贷渠道选择、信贷资金需求特性等信贷行为进行研究。在此基础上,本文通过信贷资金缺口测试的逻辑框架,运用Heckman广义三阶段回归方程对农户在正规金融市场上所受到的信贷约束程度以及信贷资金缺口进行估计,并对估计结果进行相应的解释。     

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.     

The Role of Collateral in the Credit Acquisition Process: Evidence from SME Lending

This study tests the simultaneous impact of observed characteristics and private information on debt term contracts in a multi‐period setting, using a dataset of 12,666 credit approvals by one major Portuguese commercial bank during 2007–2010. The main results show that borrowers with good credit scores that know they have a high probability of success and are unlikely to default are more willing to pledge collateral in return for a lower interest rate premium (IRP). Furthermore, lenders tailor the specific terms of the contract, increasing both collateral requirements and the IRP from observed risk, for borrowers operating in riskier industries and with less credit availability. The results are robust to controls for joint debt terms negotiation and the degree of collateralization offered by the borrower.     

Credit ratings and convertible bond prices: a simulation-based valuation

This study presents a simulation-based model of convertible bond prices under the assumption of stochastic interest rates. The model is developed such that the convertible bond price explicitly depends on the credit rating at the time of issuance. Key ideas explored in this study include terminating the simulated sample path immediately when the issuer defaults on the bond at time t, which is the same as the investor and the issuer optimally exercising their options and discounting the resulting cash flows at a risk-free rate. In turn, the defaulted group of sample paths belongs to the bottom xth percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm that has the same rating as the issuer. Upon calibrating the model, we can see that the moneyness of convertible bonds is strongly responsible for influencing the convertible bond price when the rating changes. Furthermore, the effects of stochastic interest rates are shown to be possibly significant when the interest rate risk’s market price is not zero.