具有违约观察期公司债券的定价

借助于美国破产保护法第十一章,违约公司获得-个额外的违约观察期过程,通过纳什均衡原理对股东和债权人的利益进行重新分配,利用巴黎型期权的定价思想来刻画具有这种违约观察期过程的股票与公司债券的定价模型,并从股东权益最大化,把股票的定价模型归结为-个自由边界问题,进而通过偏微分方程方法(PDE)推出股票与公司偾券价格的闭合表达式和最佳违约边界解的显式表达式;同时文章还对公司的最优杠杆,清算概率和信用利差进行讨论.     

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.     

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.     

企业信息不完全情况下的首次通过违约概率模型

基于Merton的结构化模型,利用几何布朗运动理论建立了不完全信息条件下的企业首次通过违约概率模型.根据企业的财务报表及信用记录,提出了一种新的不完全信息假设;在模型上引入股票的流通性价值,并改进其基于Merton模型的度量方法,使其适用于首次通过模型并求得内生违约边界,利用此边界给出了不完全信息条件下的企业违约概率,并分析了股票流通价值和股价与企业资产的相关关系对违约概率的影响.     

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.     

基于最优负债系数的上市银行违约概率测算模型与实证

当上市银行的长期负债系数γ的取值不同时,应用KMV模型测算出的银行违约概率大相径庭。根据债券的实际信用利差可以推算出上市银行的违约概率PDi,CS,根据长期负债系数γ可以运用KMV模型确定上市银行的理论违约概率PDi,KMV。本文通过理论违约率与实际违约率的总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型的最优长期负债γ系数;通过最优长期负债系数γ建立了未发债上市银行的违约率测算模型、并实证测算了我国14家全部上市银行的违约概率。本文的创新与特色一是采用KMV模型计算的银行违约概率PDi,KMV与实际信用利差确定的银行违约概率PDi,CS总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型中的最优长期负债γ系数;使γ系数的确定符合资本市场利差的实际状况,解决了现有研究中在0和1之间当采用不同的长期负债系数γ、其违约概率的计算结果截然不同的问题。二是实证研究表明,当长期负债系数γ=0.7654时,应用KMV模型测算出的我国上市银行违约概率与我国债券市场所接受的上市银行违约概率最为接近。三是实证研究表明国有上市银行违约概率最低,区域性的上市银行违约概率较高,其他上市银行的违约概率居中。     

基于分数布朗运动的贷款信用担保定价

上市公司对外做贷款的信用担保或相互做信用担保在我国资本市场是很普遍的现象.在贷款到期时,可能发生违约情况.信用担保本质上是看跌期权.假设上市公司净资产价格服从分数布朗散运动,采用拟鞅定价的方法,得到了公司提供信用担保和相互担保在无违约和违约情形下的定价公式.     

基于马尔可夫方法的违约传染平均域模型

基于平均域模型,将信用组合分为几个同质的子组合,假设组合中各公司的违约强度不仅取决于宏观经济状况,而且依赖于这些子组合中违约公司的数目,以刻画不同公司间的违约相互作用;并据此建模组合违约过程为连续时间马尔可夫链,借助Kolmogorov微分方程求解信用组合损失分布;最后,通过实例计算分析传染现象对组合损失分布、风险量度的影响.     

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.     

信用违约联结票券的定价

本文从定义信用违约联结票券出发,介绍了JarrowandTurnbul(1995)违约强度模型。然后在该模型的基础上,针对不同的公司,假设违约时间独立同服从指数分布且与利率期间结构独立,分别就t=0与0     

A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.     

A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.     

The effects of asset liquidity on dynamic sell-out and bankruptcy decisions

We develop a dynamic bankruptcy model with asset illiquidity. In the model, a distressed firm chooses between sell-out and default, as well as its timing under the assumption that sell-out is feasible only at Poisson jump times, where the arrival rate of acquirers stands for asset liquidity. With lower asset liquidity, the firm increases the sell-out region to mitigate the risk of not finding an acquirer until bankruptcy. Despite the larger sell-out region, lower asset liquidity increases the default probability and decreases the equity, debt, and firm values. In the optimal capital structure, with lower asset liquidity, the firm reduces leverage, but the cautious capital structure does not fully offset the increased default risk. The stock price reaction caused by sell-out depends on the sell-out timing. When the firm’s asset value is not sufficiently high, the stock price jump size is an inverted U-shape with the economic state variable. Lower asset liquidity increases the jump size due to greater surprise. These results fit empirical observations.     

违约风险的交换期权的定价模型与解法

含交易对手违约风险的交换期权采用混合模型定价,借助公司价值模型中的补偿率,同时采用以强度为基础的违约函数来确定违约的发生.假定违约强度遵从均值回复的重随机Poisson过程：且违约强度过程与标的资产,企业价值都相关.利用等价鞅测度变换方法导出含有违约风险的交换期权的价格闭解.     

Pricing credit default swaps with a random recovery rate by a double inverse Fourier transform

We evaluate the par spread for a single-name credit default swap with a random recovery rate. It is carried out under the framework of a structural default model in which the asset-value process is of infinite activity but finite variation. The recovery rate is assumed to depend on the undershoot of the asset value below the default threshold when default occurs. The key part is to evaluate a generalized expected discounted penalty function, which is a special case of the so-called Gerber–Shiu function in actuarial ruin theory. We first obtain its double Laplace transform in time and in spatial variable, and then implement a numerical Fourier inversion integration. Numerical experiments show that our algorithm gives accurate results within reasonable time and different shapes of spread curve can be obtained.     

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。     

Decomposition of default probability under a structural credit risk model with jumps?

In this paper, we consider the default probabilities caused by a jump or by oscillation under a structural credit risk model with jumps. We study the Laplace transforms of the times of default caused by a jump and by oscillation. We derive integro-differential equations and obtain some closed-form expressions for them. By inverting them, we numerically investigate the contributions of the jump component and the diffusion component to the default under a certain choice of the jump size distribution.     

Default barrier intensity model for credit risk evaluation

We establish the Default Barrier Intensity (DBI) model, based on the conditional survival probability (also called hazard function barrier), which allows the pricing of credit derivatives with stochastic parameters. Moreover, the DBI is an analytic model which combines the structural and the reduced form approaches. It deals with the impact of the default barrier intensity on the processes around the firm. Using this model we prove the Doob–Meyer decomposition of the default process associated with the random barrier. In this framework, we present the default barrier process as the sum of its compensator (which is a predictable process) and a martingale related to the smallest filtration making the random barrier a stopping time. Furthermore, the DBI as well as the Shifted Square Root Diffusion (SSRD) Alfonsi’s model emphasizes on the dependence between the stochastic default intensity and the interest rate. This model can be useful since it can be easily generalized to all the credit derivatives products such as Collateralized Debt Obligations (CDO) and Credit Default Swaps (CDS).     

Valuing risky debt: A new model combining structural information with the reduced-form approach

A new model of credit risk is proposed in which the intensity of default is described by an additional stochastic differential equation coupled with the process of the obligor’s asset value. Such an approach allows us to incorporate structural information as well as to capture the effect of external factors (e.g. macroeconomic factors) in a both parsimonious and economically consistent way. From the practical standpoint, the proposed model offers great flexibility and allows us to obtain credit spread curves of many different shapes, including double humped term structures. Furthermore, an approximate closed-form solution is derived, which is accurate, easy to implement, and allows for an efficient calibration to realized credit spreads. Numerical experiments are presented showing that the novel approach provides a very satisfactory fitting to market data and outperforms the model developed by Madan and Unal (2000).     

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.