约化模型中含有对手风险的信用违约互换定价

在约化模型中研究了含有对手风险的信用违约互换的定价问题.通过构建信用违约互换买方、卖方和参考资产之间的衰减传染结构,借助于测度变换的方法分别导出了含有单边和双边对手风险的信用违约的定价表达式.     

双指数跳扩散模型信用违约互换短期价格研究

假设参考实体没违约时信用违约互换保护买方连续支付互换价格,导出了信用违约互换价格的表达式;对标的资产价值服从双指数跳扩散模型,得到了条件违约风险率和信用违约互换的短期价格极限.这些结果比纯扩散模型假设更符合实际.     

马氏调制强度的传染模型下CDS的CVA计算

本文考虑了具有马氏调制强度的传染模型下,信用违约互换(CDS)的双边信用估值调整(CVA).在我们考虑的模型中,利率、回收率以及CDS的买方、卖方和参照实体三方的违约强度均受宏观经济环境的影响,该经济状况由一连续时间状态的齐次马氏链所刻画.利用测度变换和累积强度的Laplace变换,我们给出了CDS合同的双边CVA的表达公式,该公式可以表示为线性常微分方程组的基本解的形式.利用所得到的公式,我们数值分析了马氏调制和违约相关性对双边CVA的影响.     

基于正态逆高斯分布的篮子违约互换定价

主要讨论单因子模型的篮子型信用违约互换定价.目的是寻找一个快捷的方法来处理违约相关问题.采用了正态逆高斯分布对违约时间进行建模,得到了违约时间分布和篮子违约互换定价公式的半分析表达式,进一步地讨论了常数因子荷载扩展到随机因子荷载的情形.最后用数值模拟方法对比了正态分布和正态逆高斯分布两种模型下首次违约互换的价格.     

基于t-Copula的一篮子信用违约互换定价模型

为了刻画分布函数的厚尾特征和违约的传染性,构建了单因子t-Copula模型,以此研究一篮子信用违约互换(BDS)的定价问题。依据风险中性定价原理和顺序统计量方法,分别得到了第k次违约和n个参照实体中m个受保护的BDS价格的解析式.为了说明定价模型的有效性,用随机模拟方法分析了相应的数值算例.     

一篮子信用违约互换定价的偏微分方程方法

通过对一篮子信用违约互换的结构性分析,在约化法框架下,用PDE方法提出一个新的计算具有违约相关性的多个公司联合生存概率的方法,在此基础上得到信用互换到期之前一篮子中违约数量的概率分布.应用这个概率分布,在条件独立的假定下,先后建立了首次违约、二次违约的信用违约互换定价模型,并用PDE方法给出了定价的显性表达式,并进一步扩展到解决m次违约的信用违约互换的定价问题.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

信用违约互换的定价方法

通过对信用违约互换的结构的分析,在Merton的结构化方法框架下,用偏微分方程求出公司的违约概率密度,最后给出信用违约互换的一种定价方法.     

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.     

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本文讨论了信用衍生产品之一的总收益互换的定价问题. 其中涉及到利率风险和违约风险, 本文利用HJM利率模型来刻画利率风险, 并利用强度模型和混合模型对违约风险进行建模. 分别考虑了违约时间与利率无关时总收益互换合约的定价问题, 以及违约时间与利率相关时总收益互换合约的定价问题, 给出了相应的定价模型, 并用蒙特卡罗模拟方法得到定价问题的数值解.     

Cure events in default prediction

This paper evaluates the resurrection event regarding defaulted firms and incorporates observable cure events in the default prediction of SME. Due to the additional cure-related observable data, a completely new information set is applied to predict individual default and cure events. This is a new approach in credit risk that, to our knowledge, has not been followed yet. Different firm-specific and macroeconomic default and cure-event-influencing risk drivers are identified. The significant variables allow a firm-specific default risk evaluation combined with an individual risk reducing cure probability. The identification and incorporation of cure-relevant factors in the default risk framework enable lenders to support the complete resurrection of a firm in the case of its default and hence reduce the default risk itself. The estimations are developed with a database that contains 5930 mostly small and medium-sized German firms and a total of more than 23000 financial statements over a time horizon from January 2002 to December 2007. Due to the significant influence on the default risk probability as well as the bank’s possible profit prospects concerning a cured firm, it seems essential for risk management to incorporate the additional cure information into credit risk evaluation.     

Forecasting probabilities of default and loss rates given default in the presence of selection

This paper offers a joint estimation approach for forecasting probabilities of default and loss rates given default in the presence of selection. The approach accommodates fixed and random risk factors. An empirical analysis identifies bond ratings, borrower characteristics and macroeconomic information as important risk factors. A portfolio-level analysis finds evidence that common risk measurement approaches may underestimate bank capital by up to 17% relative to the presented model.     

Hurdle models of loan default

Some models of loan default are binary, simply modelling the probability of default, while others go further and model the extent of default (eg number of outstanding payments; amount of arrears). The double-hurdle model, originally due to Cragg (Econometrica, 1971), and conventionally applied to household consumption or labour supply decisions, contains two equations, one which determines whether or not a customer is a potential defaulter (the ‘first hurdle’), and the other which determines the extent of default. In separating these two processes, the model recognizes that there exists a subset of the observed non-defaulters who would never default whatever their circumstances. A Box-Cox transformation applied to the dependent variable is a useful generalization to the model. Estimation is relatively easy using the Maximum Likelihood routine available in STATA. The model is applied to a sample of 2515 loan applicants for whom loans were approved, a sizeable proportion of whom defaulted in varying degrees. The dependent variables used are amount in arrears and number of days in arrears. The value of the hurdle approach is confirmed by finding that certain key explanatory variables have very different effects between the two equations. Most notably, the effect of loan amount is strongly positive on arrears, while being U-shaped on the probability of default. The former effect is seriously under-estimated when the first hurdle is ignored.     

Modelling stylized features in default rates

We propose a stochastic model for the probability of default based on diffusions with given marginal distribution and autocorrelation function. The model tries to capture stylized features observed in historical default rates and is analytically tractable. Estimation procedures and expressions for analysis and prediction are provided. Copyright © 2006 John Wiley & Sons, Ltd.     

Credit default swaps and systemic risk

We present a network model for investigating the impact on systemic risk of central clearing of over the counter (OTC) credit default swaps (CDS). We model contingent cash flows resulting from CDS and other OTC derivatives by a multi-layered network with a core-periphery structure, which is flexible enough to reproduce the gross and net exposures as well as the heterogeneity of market shares of participating institutions. We analyze illiquidity cascades resulting from liquidity shocks and show that the contagion of illiquidity takes place along a sub-network constituted by links identified as ’critical receivables’. A key role is played by the long intermediation chains inherent to the structure of the OTC network, which may turn into chains of critical receivables. We calibrate our model to data representing net and gross OTC exposures of large dealer banks and use this model to investigate the impact of central clearing on network stability. We find that, when interest rate swaps are cleared, central clearing of credit default swaps through a well-capitalized CCP can reduce the probability and the magnitude of a systemic illiquidity spiral by reducing the length of the chains of critical receivables within the financial network. These benefits are reduced, however, if some large intermediaries are not included as clearing members.     

Calibration of the default probability model

In this paper, we study the calibration problem for the Merton–Vasicek default probability model [Robert Merton, On the pricing of corporate debt: the risk structure of interest rate, Journal of Finance 29 (1974) 449–470]. We derive conditions that guarantee existence and uniqueness of the solution. Using analytical properties of the model, we propose a fast calibration procedure for the conditional default probability model in the integrated market and credit risk framework. Our solution allows one to avoid numerical integration problems as well as problems related to the numerical solution of the nonlinear equations.     

Proof complexity of propositional default logic

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen??s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti??s enhanced calculus for skeptical default reasoning.     

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.