多维仿射跳扩散模型的信用风险度量  

Measuring Credit Risk under Multidimensional Affine Jump-Diffusion Model

作　　者：邓国和 汪嘉骎 DENG Guohe;WANG Jiaqin(College of Mathematics and Statistics,Guangxi Normal University,Guilin,541004,China;Tianjin Xikang Road Business Department,GF Securities Co.Ltd.,Tianjin,300051,China)

机构地区：[1]广西师范大学数学与统计学院,桂林541004 [2]广发证券天津西康路营业部,天津300051

出　　处：《应用概率统计》2022年第5期706-722,共17页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11461008);广西自然科学基金项目(批准号:2018GXNSFAA281016)资助。

摘　　要：信用风险是银行,其他金融机构以及任何参与金融合约交易当事人关心的主要问题,构建有效的信用风险定价模型尤为重要.本文在企业总资产价值满足多维仿射跳扩散模型下建立了信用风险结构化模型,用违约概率度量企业信用风险.根据仿射结构特点,应用半鞅Itô公式,Feynman-Kac定理,Fourier反变换,以及多维特征函数等技术和方法,给出企业违约概率,违约距离和违约零息债券价格的显示解公式,并利用数值实例分析波动率、利率、跳跃强度和相关系数等模型中主要参数对违约概率的影响.研究结论对可违约债券及各类信用衍生品定价具有很强的借鉴意义.Credit risk is a major issue for Banks,other financial institutions and anyone involved in the transaction of financial contracts.It is particularly important to model an effective pricing approach for managing the credit risk.This paper establishes a credit risk model using the structural model in which the corporate’s total asset value follows multidimensional affine jump diffusion processes,and measures the corporate’s credit risk value in terms of default probability.The closed-form explicit solutions for the corporate’s default probability,distance to default and zero-coupon credit bond are obtained by means of some methods including the characteristics of affine structure,the semi-martingale Itô formula,the Feynman-Kac theorem and the Fourier inverse transformation technique.Numerical experiments are used to analyze the impacts of volatility,interest rate,jump densities,related coefficients and other parameters on the default probability.These conclusions have some key reference values for pricing the defaultable bonds and credit derivatives.

关 键 词：信用风险 多维跳扩散过程 结构化模型 FOURIER变换 数值计算 

分 类 号：O211.6[理学—概率论与数理统计] O29[理学—数学]