资产价值服从跳-扩散过程的风险债券定价

作为对结构化模型和简化模型的改进,本文将结构化模型和简化模型两者融合后提出了一种特殊的跳-扩散过程.在假设公司价值服从这一类跳-扩散过程的情况下,建立了公司风险债券价值所满足的方程,并利用鞅方法得到了公司债券的定价公式.     

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.     

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.     

双跳-扩散过程下的脆弱期权定价

本文考虑含有交易对手违约风险的衍生产品的定价,以公司价值信用风险模型为基础,在标的资产价格和公司价值均服从跳-扩散过程的情况下,运用结构化的方法对脆弱期权定价进行建模,建立了双跳-扩散过程下的脆弱期权定价模型,分别在公司负债固定和随机的情况下推导出了脆弱期权的定价公式.     

房价服从非时齐Poisson跳扩散的住房抵押贷款保证险的定价

利用期权定价理论和保险精算方法, 分析了住房抵押贷款保证险的定价问题, 给出了全额担保和部分担保两类住房抵押贷款保证险的定价公式, 其中未偿付额服从一般扩散过程, 房产价格服从带非时齐Poisson跳的扩散过程.     

服从分数跳-扩散过程的复合期权定价

用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了欧式复合期权的定价公式.结果推广了Gukhal以及Li等关于传统跳-扩散模型下的欧式复合期权的定价公式.     

连续红利支付在跳扩散模型下的再装期权的定价

本文在连续时间支付红利,且股票价格服从Poisson跳-扩散过程的假设下,建立股票价格模型,并应用保险精算法给出一类奇异期权—再装期权再装一次情况下的定价公式.     

基于FFT的区域变换对数均匀跳扩散模型期权定价

本文考虑具有区域变换跳跃幅度服从对数均匀分布的跳扩散模型的期权定价问题.本文给出了这样模型的期权定价方法和计算过程,当中采用了FFT(快速傅里叶变换法),最后给出了数值计算结果.     

随机利率情形下跳-扩散模型的未定权益定价

讨论Vasicek短期利率模型下,风险资产的价格过程服从跳-扩散过程的欧式未定权益定价问题,利用鞅方法得到了欧式看涨期权和看跌期权定价公式及平价关系,最后给出了基于风险资产支付连续红利收益的欧式期权定价公式.     

体制转换市场中股价服从带门限均值回复过程的期权定价

体制转换和门限特征是资产定价过程中的两个重要特征.本文在股价服从带门限均值回复过程而折现率含有状态切换的情况下对欧式看涨期权进行定价.首先给出股价服从无门限均值回复过程的欧式期权定价;然后,结合风险中性定价原理、超合流函数、Laplace变换等方法,给出股价服从一般情形的Volterra积分形式的欧式期权定价公式.为了进一步说明所得结论的适用性,本文最后给出了欧式看涨期权定价的差分格式解.     

Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

传统的保险市场难以满足日益频发的巨灾风险分散需求,巨灾债券作为一种非传统金融创新工具提供了一种新的分散机制,而精准定价则对巨灾债券的成功发行与交易起着关键作用。本文基于风险中性测度技术,在Longstaff随机利率且巨灾风险累积损失服从复合泊松损失条件下,得到了零息票巨灾债券价格公式;进一步结合广东省1989~2015年台风风暴潮灾害损失数据进行实证分析;最后,针对定价公式复杂性,本文利用快速傅里叶变换方法进行数值求解,结果验证了本文所构模型的可行性。本文的研究是希望能为我国发行巨灾债券与风险测度提供一定的理论基础与技术支持。     

Լ��ģ���к��н��׶������÷��յĿ�ת��ծȯ�Ķ���

??This paper studies the price of convertible bonds with counterparty credit risk in a reduced-form model. We suppose that the default intensity process and the interest rate process follow the Vasicek model, and derive the price expression of convertible bonds using the method of measure changes. Moreover, we make some numerical analysis on the explicit formulae to demonstrate the sensitivity of a convertible bond price to changes in the parameters of the model.     

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.     

On reduced-form intensity-based model with ‘trigger’ events

Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts of both observable ‘trigger’ events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with ‘trigger’ events. Both single-default and multiple-default cases are considered in this paper. In the former case, a simple expression for the distribution of the default time is obtained. Applications of the proposed model to price defaultable bonds and multi-name Credit Default Swaps are provided.     

跳-扩散结构下内含巴黎期权特征的可转债定价研究

考虑了跳-扩散结构下的可转换债券定价问题.首先分析了回售、赎回等条款,发现可转换债券具有巴黎期权特征.然后,根据期权定价理论,运用近似对冲跳跃风险的方法,建立了可转换债券的定价模型,得到了可转换债券价格所满足的偏微分方程.基于半离散化方法,给出了偏微分方程求解的数值方法,并且对数值方法的稳定性和误差进行了分析.最后,以重工转债和南山转债为例,对可转债市场进行了实证研究.     

A mathematical model for weighing investments

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.     

随机利率模型下基于Tsallis熵分布的可转债定价

本文主要研究基于Tsallis熵分布且存在瞬时违约风险的情况下,随机利率服从Vasicek利率模型的可转换债券的定价问题。标的股票价格过程服从Tsallis熵分布的前提下,构建投资组合,利用无套利原理得到可转债价格所满足的偏微分方程,进一步采用有限元法得到可转债价格的数值解。根据长江证券、利欧股份以及吉林敖东股票的市场真实数据,利用Tsallis熵分布模拟收益率序列,并得到基于Tsallis熵分布的股价模型优于几何布朗运动模型下的最优参数,在此基础上,绘制股价基于Tsallis熵分布下三种标的股票所对应可转债的理论价格的三维图及与市场实际价格的对比图。研究结果发现,对应标的股票价格基于Tsallis熵分布下的可转债理论价格与市场真实价格更为接近。     

Existence and Regularity for Dynamic Viscoelastic Adhesive Contact with Damage

A model for the dynamic process of frictionless adhesive contact between a viscoelastic body and a reactive foundation, which takes into account the damage of the material resulting from tension or compression, is presented. Contact is described by the normal compliance condition. Material damage is modelled by the damage field, which measures the pointwise fractional decrease in the load-carrying capacity of the material, and its evolution is described by a differential inclusion. The model allows for different damage rates caused by tension or compression. The adhesion is modelled by the bonding field, which measures the fraction of active bonds on the contact surface. The existence of the unique weak solution is established using the theory of set-valued pseudomonotone operators introduced by Kuttler and Shillor (1999). Additional regularity of the solution is obtained when the problem data is more regular and satisfies appropriate compatibility conditions.     

Analytical pricing of defaultable discrete coupon bonds in unified two-factor model of structural and reduced form models

Pricing formulae for defaultable corporate bonds with discrete coupons (under consideration of the government taxes) in the united two-factor model of structural and reduced form models are provided. The aim of this paper is to generalize the two-factor structural model for defaultable corporate discrete coupon bonds (considered in [1]) into the unified model of structural and reduced form models. In our model the bond holders receive the stochastic coupon (which is the discounted value of a predetermined value at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered. The expected default event occurs when the equity value is not sufficient to pay coupon or debt at the coupon dates or maturity and the unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We provide the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration.