随机利率下的可分离债券的定价

假设股票价格服从对数正态分布,利率是随机的,且股票价格的波动率,无风险利率均为时间的确定性连续函数,通过选取不同的计价单位及概率测度的变换,利用鞅的方法研究了随机利率下的可分离债券的定价,并得到了可分离债券的定价公式.     

连续时间下的可分离债券的定价

假设股票价格服从对数正态分布,且股票价格的波动率,无风险利率均为时间的确定性连续函数,利用鞅的方法研究了连续时间下的可分离债券的定价,并得到了可分离债券的定价公式.     

可转换债券:参数估计与定价实证

金融产品的定价,是金融工程研究的核心问题之一,同样可转换债券的定价也引起国内外学者们的关注.本文试图借鉴国内外研究成果,在分析股价及利率特性的基础上,运用推导出基于股价和利率的双因素定价模型;从中国实情出发,运用广义自回归条件异方差模型(简称GARCH)得出长期波动率,通过将可转债条款转化为边界终值条件并利用数值方法对可转债定价.     

基于路径积分方法的可转换债券定价

可转换债券是一种混合金融衍生品,主要特点是在某时刻可以转换成其他金融产品,保障双方收益.假设利率服从Vasicek随机利率模型和股票价格服从几何布朗运动过程,利用Feynman路径积分方法分别重构债券和转股期权的定价函数给出可转债定价体系新的估值模型.通过数值模拟说明解析公式的计算结果更稳定,能够降低可转债高估的风险.     

随机利率下服从指数O-U过程的可转换债券的鞅定价

从定量的角度分析了随机利率下有股利分配的可转换债券的价值构成,并在股价服从广义O-U过程的条件下,利用鞅定价方法推导出可转换债券的定价公式.     

随机利率下有股利分配的可转换债券的鞅定价

从定量的角度分析了随机利率下有股利分配的可转换债券的价值构成, 并在股票价格服从对数正态分布的条件下, 利用Martingale Pricing方法推导出其定价公式.     

分数布朗运动下可分离交易可转债的定价

假定利率满足Vasicek模型和标的股票的价格遵循分数布朗运动的条件下,建立了分离交易的可转换公司债券的的定价模型,并利用风险中性定价原理推导出其定价公式.最后,所做模拟研究表明分数布朗运动下可分离交易可转债的定价模型是合理的.     

带有信用风险的可转换债券的定价模型

本介绍了带有随机利率和破产风险等几种信用模型下的可转换债券的定价模型和相关的计算方法。在一般的cox模型下，得到了某种意义下的显式公式和偏微分方程，为数值算法建立了理论基础。     

约化模型中含有交易对手信用风险的可转换债券的定价

本文在约化模型中研究了含有交易对手信用风险的可转换债券的定价问题.我们假设市场中可转换债券的违约强度过程和无风险利率过程均满足Vasicek模型,通过引入测度变换的方法导出了该模型中可转换债券的定价表达式.此外,我们通过数值分析展示了模型的参数变化对可转换债券价值的影响.     

提前还贷及其隐含期权的分析

可提前还款的定期贷款是隐含着期权的利率衍生物，本文建立CIR利率模型下可提前还款的定期贷款的数学模型，通过离散偏微分方程，建立了模型的计算方法，讨论了随机利率对提前还贷的影响．     

可转换债券价值确定的蒙特卡罗方法

首先对可转换债券定价的各种数值方法作了研究综述,并比较了各种方法的优点和缺陷;针对可转换债券品种价值确定过程中的特征,介绍了采用蒙特卡罗仿真算法为可转换债券定价的实施步骤,根据可转换债券持有、转股、赎回和回售等可能发生的状况,分别给出了用该方法实现定价的原理和过程.     

运用非均匀三次B样条拟合我国国债利率期限结构

运用非均匀三次B样条作为拟合函数,以我国上海证券交易所附息国债的日价格为数据,拟合了我国国债的利率期限结构.实证结果显示,使用"等额现金量法"来确定样条节点向量,所拟合出的我国国债利率期限结构符合经济原理,且对债券价格的估计误差较小.     

可转换债券向下修正条款触发与股价异常回报的关联研究

向下修正条款是可转换债券募集条款中的一项触发性条款。本文以向下修正条款的触发与可转换债券发行公司的股票价格异常回报的关联程度为研究目的,分别采用传统和修正的事件研究法,对可转换债券向下修正的频率及其对股价影响的幅度和深度进行了研究。分析结果说明,没有明显的证据支持样本公司向下修正转股价行为会影响股票价格的波动。通过比较样本公司条款的异同,结合实证研究结论,本文给出了未来可转换债券向下修正转股价条款设计原则和建议。     

Books in Brief

Abstract

Prisoners of Silence: Breaking the Bonds for Adult Illiteracy in the United States by Jonathan kozol. New York: Continuum, 113 pages, $8.95.

Happier by Degrees by Pam Mendelsohn. New York: E.P. Dutton, 302 pages, $13.95 ($7.95 paperback).

The Kent State Coverup by Joseph Kelner and James Munves. New York: Harper and Row, 305 pages, $15.00     

Drawdown: from practice to theory and back again

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive homogenous risk measure, so that it can be linearly attributed to factors; and convex, so that it can be used in quantitative optimization. We empirically explore the differences in risk attributions based on CED, Expected Shortfall (ES) and volatility. An important feature of CED is its sensitivity to serial correlation. In an empirical study that fits AR(1) models to US Equity and US Bonds, we find substantially higher correlation between the autoregressive parameter and CED than with ES or with volatility.     

Asymptotic expansions and Richardson extrapolation of approximate solutions for integro-differential equations by mixed finite element methods

In this paper asymptotic error expansions for mixed finite element approximations of the integro-differential equation are derived, and Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation post-processing technique. The results of this paper provide new asymptotic expansions. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a-posteriori error estimators for this mixed finite element method. Finally, a numerical example is provided to validate the theoretical results. This project was supported in part by the Special Funds for Major State Basic Research Project (2007CB8149), the National Natural Science Foundation of China (10471103 and 10771158), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), the NSERC, Tianjin Natural Science Foundation (07JCYBJC14300), Tianjin Educational Committee, Liu Hui Center for Applied Mathematics of Nankai University and Tianjin University, and Tianjin University of Finance and Economics.     

Optimale Portefeuilles für Institutionelle Anleger

Zusammenfassung Mit Hilfe der Standardmethode von Markowitz werden optimale Portefeuilles für Pensionskassen und Lebensversicherungen aufgrund von schweizerischem Datenmaterial beberechnet. Dem Umstand, daß es sich um institutionelle Anleger handelt, wird durch die Wahl der Daten Rechnung getragen. Es stellt sich heraus, daß die optimalen Portefeuilles sowohl bei einer nominellen als auch bei einer realen Zielsetzung stets einen geringen Aktienanteil aufweisen. Zudem fällt der Effizienzverlust, welcher aus einer nominellen Zielsetzung der institutionellen Anleger und einer realen Zielsetzung der Versicherten resultiert, extrem klein aus.

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Summary This study analyzes optimal portfolios for pension funds and life insurance compagnies. Portfolios optimal in real or nominal terms are calculated by Markowitz' method using Swiss data. The characteristics of Swiss institutional investors were taken into account by choosing the specific data. The main results are as follows: 1) Common stocks play a minor roll in efficient portfolios. Bonds and real estate dominate. 2) The efficiency loss due to optimizing in nominal terms (as institutional investors tend to do) rather than real terms (as the insured would possibly favor) is extremely small.

     

基于或有可换债的PPP项目资本证券化研究

PPP项目具有的“大而不倒”特性,致使其陷入财务困境时,政府不得不介入和对其进行救助。然而这种救助必然会扭曲PPP项目定价和加剧市场的不正当竞争。为对冲PPP项目资本短缺的风险及抑制项目“大而不倒”负面效应,建议社会资本方发行或有可换债(CEBs)。CEBs在可换债的基础上引入或有可转债的条款,使其具有危机救助功能和风险转移功能。且CEBs的发行不会增加项目运营公司的公司债务。只有当项目因资本短缺而陷入财务困境时,社会资本方可以通过CEBs转为项目特定收益权和债务减记的方式来增加可支配资本,以维持PPP项目正常运营。研究表明,CEBs通过类似保险的形式对冲项目的资本短缺的风险;为社会资本提供合理的退出机制;对冲政府的裸露头寸。     

Superconvergence estimates of finite element methods for American options

In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp L ²-, L ^∞-norm error estimates and an H ¹-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator. This work was supported in part by the National Natural Science Foundation of China (10471103 and 10771158), the National Basic Research Program (2007CB814906), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), Tianjin Natural Science Foundation (07JCY-BJC14300), and Tianjin University of Finance and Economics.     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.