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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.     

一般均衡下基于产品市场和资本市场的单名CDS定价

次贷危机呼吁新的信用衍生品定价模型, 因此为存在产品市场和资本市场的经济结构建立一般均衡的单名CDS定价模型, 使用最优化求解一般均衡下的商品价格和CDS价格. 可以发现一般均衡的CDS定价具有资本市场和产品市场的因素, 这表示CDS的价格不再是由单纯的资本市场因素决定的, 而是由无风险利率、资本产出弹性、违约率、回收率同时决定的. 通过数量约束用模拟的方式研究多个均衡的动态变化, 发现违约风险的增加使得价格剧烈波动且市场交易萎缩. 在为以中国工商银行为参考资产的CDS定价过程中, 发现各种因素在不同的时期都可能成为定价的主要影响因素. 可以发现, 次贷危机的定价体系存在着信用调整问题和定价与实体经济脱节的问题. 可以认为, 一般均衡下基于产品市场和资本市场的单名CDS定价可以囊括多个市场的交叉影响, 为衍生品定价提供一个新的方向.     

人民币利率互换中风险的市场价格

为研究人民币利率互换市场中流动性风险和违约风险的市场价格,运用三因子广义高斯仿射模型,同时对人民币国债市场利率、银行间质押式回购市场利率和利率互换市场利率进行模拟,并采用极大似然估计方法估计众多参数。结果发现,在目前的人民币利率互换定价过程中,流动性要素相对违约要素更加重要,市场给予流动性风险以显著的风险溢价。如采用互换利差定价法为人民币利率互换定价的话,可以以回购利率作为基准,在此基础上考虑信用风险来进行。     

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.     

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.     

债券定价及利率风险的市场价格的重构方法

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.     

我国期货市场违约风险的研究

引入违约距离的概念,建立了期货市场违约风险评估模型,采用GARCH-M模型对期货合约价格收益的波动率进行估计.运用此模型研究了郑州商品交易所上市品种小麦的违约风险,所得结果与实际市场结果相吻合.因此,可以运用本文提出的期货市场违约风险评估模型能预测临近交割月时期货市场发生违约的概率,实时捕捉期货市场发生违约事件的信息.     

约化模型下具有信用风险的交换期权定价

考虑约化模型下具有信用风险的交换期权的定价问题.假设市场中无风险利率服从Vasicek模型,违约强度过程服从跳扩散模型.通过选取合理的等价测度,得到期权价格的封闭解.     

具有随机利率的跳扩散模型下的脆弱期权的定价

本文研究了具有随机利率的跳扩散模型下考虑违约风险的欧式看涨和看跌期权的定价问题.当标的资产价值和交易对手的资产价值均服从含有共同跳跃的跳扩散模型,以及利率服从Vasicek模型时,利用跳扩散模型的Girsanov定理,给出了脆弱欧式看涨和看跌期权价格的显示表达式.     

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。     

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.     

基于区间数DEA的贷款定价模型研究

在贷款的买方市场或充分竞争的金融环境中,贷款利率不会由银行自己说了算,因此建立银企双方共同接受的贷款利率定价模型在现实中尤为重要。本文采用区间数的形式反映存款利息支出率、违约风险补偿率等定价指标的不确定性,以已结清贷款最小定价效率、最大定价效率组成的贷款定价效率区间为目标,以新贷款的贷款利率为决策变量,通过逆向求解区间数DEA模型反推出新贷款的贷款利率区间,建立了基于区间数DEA的贷款定价模型。本文的创新与特色一是以已结清贷款的存款利息支出率、目标利润率等指标为输入,以已结清贷款的贷款利率为输出,利用DEA模型求得已结清贷款的实际最小效率及最大效率。二是以银企双方均可接受的贷款定价效率区间为目标、以新贷款的存款利息支出率等用区间数形式表示的贷款成本为投入,反推出贷款利率的取值区间。三是通过区间数形式来反映违约风险补偿率、目标利润率等定价指标的不确定性,改变了现有研究将目标利润、贷款费用、违约损失等变量看作常数来定价的不合理现状。研究表明:存款利息支出率、费用支出率、违约风险补偿率及目标利润率均与贷款利率成正比。企业提高在贷款银行中的资金结算比率、存贷比率可以降低贷款利率。     

Interest rate swap pricing with default risk under variance gamma process

Under the assumption that the dynamic assets price follows the variance gamma process, we establish a new bilateral pricing model of interest rate swap by integrating the reduced form model for swap pricing and the structural model for default risk measurement. Our pricing model preserves the simplicity of the reduced form model and also considers the dynamic evolution of the counterparty assets price by incorporating with the structural model for default risk measurement. We divide the swap pricing framework into two parts, simplifying the pricing model relatively. Simulation results show that, for a one year interest rate swap, a bond spread of one hundred basis points implies a swap credit spread about 0.1054 basis point.     

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.     

Restructuring risk in credit default swaps: An empirical analysis

This paper estimates the price for restructuring risk in the US corporate bond market during 1999–2005. Comparing quotes from default swap (CDS) contracts with a restructuring event and without, we find that the average premium for restructuring risk represents 6%–8% of the swap rate without restructuring. We show that the restructuring premium depends on firm-specific balance-sheet and macroeconomic variables. And, when default swap rates without a restructuring event increase, the increase in restructuring premia is higher for low-credit-quality firms than for high-credit-quality firms. We propose a reduced-form arbitrage-free model for pricing default swaps that explicitly incorporates the distinction between restructuring and default events. A case study illustrating the model’s implementation is provided.     

A pricing model for secondary market yield based floating rate notes subject to default risk

The purpose of this article is to price secondary market yield based floating rate notes (SMY-FRNs) subject to default risk. SMY-FRNs are derivatives on the default-free term structure of interest rates, on the term structures for default-risky credit classes, and on the structure of a determined pool of bonds. The main problem in SMY-FRN pricing (as compared to the pricing of standard interest rate or credit derivatives) is market incompleteness, which makes traditional no-arbitrage pricing by replication fail. In general, SMY-FRNs are subject to two types of default risk. First, the SMY-FRN issuer may go bankrupt (direct default risk). Second, the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the SMY-FRN coupons (indirect default risk). This article is the first one which provides a no-arbitrage pricing model for SMY-FRNs with direct and indirect default risks. It is also the first article applying incomplete market pricing methodology to SMY-FRNs.     

Estimation and evaluation of the term structure of credit default swaps: An empirical study

Chen, Cheng, Fabozzi and Liu [Chen, Ren-Raw, Cheng, Xiaolin, Fabozzi, Frank, Liu, Bo, 2008. An explicit, multi- factor credit default swap pricing model with correlated factors. J. Financial Quantitative Anal. 43 (1), 123-160] provide an explicit solution to the value of the credit default swap when the interest rate and the hazard rate are correlated. They also provide empirical evidence to support the model with transaction prices. In this paper, we extend their empirical work to study the term structure of CDS spreads by using a matrix CDS dataset from J. P. Morgan Chase. Matrix data contain interpolated prices based on traders’ expectations, which are often criticized as being “unreal”. However, the benefit of this matrix dataset is that it contains the entire credit spread curves, which allows us to understand the cross-sectional variation of the credit risk. The empirical results show that the parameters of the model are highly significant and it captures most of the cross-sectional as well as time series variation.