具有一般跳幅度分布的跳扩散模型下永久公司债券的定价

在公司资产价值演化服从具有一般跳幅度分布的跳扩散模型下,采用结构化方法研究具有无限到期日公司债券的定价问题,通过微分方程的方法和无套利原理获得了公司债券,股东权益和公司总价值的定价表达式以及最佳违约边界的表达式.     

一类杠杆公司的破产概率:回望期权定价方法

利用结构化方法构造了杠杆公司的金融资产组合,由于公司破产的不可逆性和不确定性,可以把公司破产理解为公司所发行的债券发生违约.通过求解回望期权所满足的抛物型随机偏微分方程,推导出了混合分数跳-扩散模型下杠杆公司的股票定价公式,给出了杠杆公司在财务出现危机时股东通过资本注入来弥补经营损失和清偿债务而没有导致公司破产的概率,...     

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。     

基于权益再融资与策略性债务支付的公司财务困境纾解研究

为了应对公司财务困境问题,在兼顾股东与债权人利益的基础上,采用激励相容理论,构建了基于权益再融资和策略性债务支付的公司定价模型,厘清了权益再融资、债务重组、财务困境及其伴生的再谈判之间的关系,据此提出了一种公司财务困境纾解方案。特别地,给出了策略性债务支付下进行权益再融资的可行性依据,并辅以再谈判手段及股东、债权人双方利益最大化目标,确定了最优重组边界及最优减记息票。分析结果表明:①将策略性债务支付置于财务困境之后、兼容权益再融资的综合方案,可在一定程度上避免策略性债务支付行为的投机性所导致的对公司定价的高估,产生了在一定条件下增加债务价值、放缓信用价差增长速度的效果;②权益再融资成本与信用价差之间呈现倒U型关系;③基于纳什均衡博弈的策略性债务支付减记息票不受流动性及权益再融资的影响,并可保证其处于公司的支付能力之内。     

Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Föllmer–Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Lévy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.     

具有跳扩散模型下永久公司债券的定价和最佳资产结构

综合运用偏微分方程方法和结构化方法,在公司资产价值演化服从跳扩散模型下,研究永久公司债券的定价问题和最佳资产结构问题,获得了公司债券,股东权益和公司总价值的定价表达式和最佳杠杆比率的表达式.     

Multiscale Intensity Models for Single Name Credit Derivatives

We study the pricing of defaultable derivatives, such as bonds, bond options, and credit default swaps in the reduced form framework of intensity‐based models. We use regular and singular perturbation expansions on the intensity of default from which we derive approximations for the pricing functions of these derivatives. In particular, we assume an Ornstein‐Uhlenbeck process for the interest rate, and a two‐factor diffusion model for the intensity of default. The approximation allows for computational efficiency in calibrating the model. Finally, empirical evidence on the existence of multiple scales is presented by the calibration of the model on corporate yield curves.     

多重可违约基金的定价

In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs. Generally,The risk-neutral default intensity χ^Q is not equal to the empirical or actual default intensity λ,. This paper proves that multiple default intensities are invari-ant under equivalent martingale transformation,given a well-diversified portfolio corresponding to the defaultable bond. Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims.     

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.     

A latent process model for the pricing of corporate securities

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status is assumed to be latent or unobservable, and default occurs when the firm status process reaches a default threshold at the first time. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. Our model can evaluate both the corporate debt and equity to fit their market prices in a unified framework. When the two processes are perfectly correlated, our model is reduced to the seminal Black–Cox model. Numerical examples are given to support the usefulness of our model. A previous version of this paper was presented at the Tsukuba–Stanford workshop held at Stanford University on March 2006. The authors are grateful to participants of the workshop for helpful discussions.     

Market implied volatilities for defaultable bonds

Typically, implied volatilities for defaultable instruments are not available in the financial market since quotations related to options on defaultable bonds or on credit default swaps are usually not quoted by brokers. However, an estimate of their volatilities is needed for pricing purposes. In this paper, we provide a methodology to infer market implied volatilities for defaultable bonds using equity implied volatilities and CDS spreads quoted by the market in relation to a specific issuer. The theoretical framework we propose is based on the Merton’s model under stochastic interest rates where the short rate is assumed to follow the Hull–White model. A numerical analysis is provided to illustrate the calibration process to be performed starting from financial market data. The market implied volatility calibrated according to the proposed methodology could be used to evaluate options where the underlying is a risky bond, i.e. callable bond or other types of credit-risk sensitive financial instruments.

     

Pricing model of interest rate swap with a bilateral default risk

Under the foundation of Duffie & Huang (1996) [7], this paper integrates the reduced form model and the structure model for a default risk measure, giving rise to a new pricing model of interest rate swap with a bilateral default risk. This model avoids the shortcomings of ignoring the dynamic movements of the firm’s assets of the reduced form model but adds only a little complexity and simplifies the pricing formula significantly when compared with Li (1998) [10]. With the help of the Crank-Nicholson difference method, we give the numerical solutions of the new model to study the default risk effects on the swap rate. We find that for a one year interest rate swap with the coupon paid per quarter, the variance of the default fixed rate payer decreases from 0.1 to 0.01 only causing about a 1.35%’s increase in the swap rate. This is consistent with previous results.     

On absolutely continuous compensators and nonlinear filtering equations in default risk models

We discuss the pricing of defaultable assets in an incomplete information model where the default time is given by a first hitting time of an unobservable process. We show that in a fairly general Markov setting, the indicator function of the default has an absolutely continuous compensator. Given this compensator we then discuss the optional projection of a class of semimartingales onto the filtration generated by the observation process and the default indicator process. Available formulas for the pricing of defaultable assets are analyzed in this setting and some alternative formulas are suggested.     

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.     

Credit Derivatives Pricing Based on Lévy Field Driven Term Structure

We use Lévy random fields to model the term structure of forward default intensity, which allows to describe the contagion risks. We consider the pricing of credit derivatives, notably of defaultable bonds in our model. The main result is to prove the pricing kernel as the unique solution of a parabolic integro-differential equation by constructing a suitable contractible operator and then considering the limit case for an unbounded terminal condition. Finally, we illustrate the impact of contagious jump risks on the defaultable bond price by numerical examples.     

跳-扩散过程下具有目标杠杆比率的违约风险模型

本文在研究公司债务违约风险时,假设公司价值的动态变化服从跳-扩散过程;假设公司可以根据公司价值的变化调整其债务水平,因而存在公司的目标杠杆比率,违约边界定义为公司历史价值的对数加权平均;当公司价值下降到违约边界时发生债务违约.数值模拟表明公司债务的信用利差对公司的目标杠杆比率和跳过程的强度具有高度的敏感性.本文的模型解决了在长期和短期信用利差预测时结构化模型和约化模型存在的缺陷.     

A simple model of deferred callability in defaultable debt

Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly to most corporate debt, includes an embedded issuer’s call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generating a protection period. We value the call feature as a European option on perpetual defaultable debt. We do this by first modifying the underlying asset process to incorporate a time-dependent bankruptcy level before the expiration of the embedded option. We identify a call option on debt as a fixed number of put options on a modified asset, which is lognormally distributed, as opposed to the market value of debt. To include the possibility of default before the expiration of the option we apply barrier options results. The formulas are quite general and may be used for valuing both embedded and third-party options. All formulas are developed in the seminal and standard Black–Scholes–Merton model and, thus, standard analytical tools such as ‘the greeks’, are immediately available.     

非系统风险与公司最优资本结构

公司经常面临巨大的非系统风险,而现行的资本结构理论很少涉及非系统风险对融资决策的影响.由此,基于效用无差别定价原理,运用随机控制和最优停时理论,研究由股权资本持有人决定违约时间的股权价值和债权价值,分析最优资本结构,计算最优破产策略.结果表明:适当的股权和债权的融资组合可以分散公司非系统风险,而对于谨慎型投资者,债权分散公司风险的作用减弱;投资者的风险态度对破产选择、股权价值有显著影响,对债权价值影响较小;通过实证估计绝对风险厌恶系数是一个可行的计量方法.     

基于动态演化博弈分析的投贷联动创新机制研究

通过一个包含股权投资公司、商业银行以及政府三方主体的动态演化博弈模型,建立了一种由政府引导的投贷联动创新机制。理想状态下,科创企业能够获得商业银行的信贷支持,非科创企业能够通过股权融资降低财务杠杆,政府则通过对投贷联动进行协调获得更高的税收与股权投资收益。研究发现,政府在进一步推动投贷联动中发挥着不可替代的重要作用,提高项目质量、提高对非科创企业的价值提升能力以及适当的政府干预是推动投贷联动顺利开展的三条重要路径。研究结论对进一步推动供给侧结构性改革,缓解科创企业融资困境,降低企业杠杆率具有一定的参考价值。     

A Simple Novel Approach to Valuing Risky Zero Coupon Bond in a Markov Regime Switching Economy

We have addressed the problem of pricing risky zero coupon bond in the framework of Longstaff and Schwartz structural type model by pricing it as a Down-and-Out European Barrier Call option on the company’s asset-debt ratio assuming Markov regime switching economy. The growth rate and the volatility of the stochastic asset debt ratio is driven by a continuous time Markov chain which signifies state of the economy. Regime Switching renders market incomplete and selection of a Equivalent martingale measure (EMM) becomes a subtle issue. We price the zero coupon risky bond utilizing the powerful technique of Risk Minimizing hedging of the underlying Barrier option under the so called “Risk Minimal” martingale measure via computing the bond default probability.