Vasicek利率模型下带有零息票债券的投资-消费模型

应用随机最优控制理论研究Vasicek利率模型下的投资-消费问题,其中假设无风险利率是服从Vasicek利率模型的随机过程,且与股票价格过程存在一般相关性.假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成,投资者的目标是最大化中期消费与终端财富的期望贴现效用.应用变量替换方法得到了幂效用下最优投资-消费策略的显示表达式,并分析了最优投资-消费策略对市场参数的灵敏度.     

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。     

Ho-Lee利率模型下多种风险资产的动态投资组合

假设无风险利率可由Ho-Lee利率模型描述,且与股票动态存在一般线性相关系数,应用最优性原理和HJB方程研究了市场存在多种风险资产情形的动态资产分配问题,通过变量替换方法得到了幂效用和指数效用下最优投资策略的显示解,数值算例分析了利率参数和市场参数对最优投资策略的影响趋势。研究结果发现:两种效用下的最优策略均由两部分所构成,一部分由市场参数所确定,另一部分由利率参数所确定。而且,幂效用下的最优投资策略与瞬时利率无关,而指数效用下的最优投资策略与瞬时利率相关。     

固定执行价格下回望看涨期权保险精算定价

利用保险精算方法,将期权定价问题转化为纯保费确定问题,根据股票价格过程的实际概率测度推导出了无风险利率为常数时,固定执行价格下回望看涨期权定价公式,验证了当标的资产的期望收益率等于无风险利率时,保险精算定价和风险中性定价的一致性.最后通过实例分析了保险精算价格和风险中性价格的差异,并利用Matlab编程得到了保险精算价格与标的资产期望收益率之间的关系.     

在单因素HJM结构下定价两种汇率连动期权

汇率连动期权是一种未定权益,其投资者不得不同时规避国外股票和外汇价格变动的风险.本文讨论两种汇率连动期权:一种汇率期权,连动国外股票价格的变化;一种写在国外股票上的固定汇率期权,在到期的时候,利用预先约定的汇率将期权的价值转换为国内的货币价值.在利率和汇率同时随机的情况下,本文得到了这两种看涨期权价格的精确解.更进一步,通过得到看涨-看跌期权的平价公式,本文也获得了看跌的汇率连动期权的价格.     

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.     

跳扩散模型中随机利率下的两种奇异期权定价

假定基础资产股票价格的跳过程为比Poisson过程更一般的跳过程-一类特殊的更新过程,在风险中性的假设下,利用鞅方法推导出了在随机利率下的两种奇异期权定价公式.     

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。     

随机利率下基于Tsallis熵分布的幂式期权定价

考虑到无风险利率的随机性以及股票收益率分布的尖峰厚尾和长期相依性,利用具有长程记忆及统计反馈性质的Tsallis熵分布建立股票价格的运动模型,在无风险利率服从Vasicek模型下,运用保险精算定价法得到了幂式期权的定价公式,推广了经典的Black-Scholes定价公式,扩展了已有文献的结论.     

基于二次效用函数的投资组合问题研究

设无风险利率、股票收益率和波动率都是一致有界随机过程,在股票价格服从跳跃一扩散过程时,同时考虑具有随机资金流的介入,研究了二次效用的动态投资组合选择优化问题,通过随机线性二次控制和倒向随机微分方程得到了最优投资组合策略的解析表达式.     

广义Black-Scholes模型期权定价新方法--保险精算方法

利用公平保费原则和价格过程的实际概率测度推广了Mogens Bladt和Tina Hviid Rydberg的结果．在无中间红利和有中间红利两种情况下，把Black-Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况，在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系．给出了风险资产(股票)具有随机连续复利预期收益率和随机波动率的广义Black-Scholes模型的期权定价的一般方法．利用保险精算方法给出了股票价格遵循广义Ornstein-Uhlenback过程模型的欧式期权的精确定价公式和买权和卖权之间的平价关系．     

分数次布朗运动环境中的有交易成本的上限型买权的期权定价

本文在标的资产价格服从几何分数次布朗运动假设下,在无风险利率和红利率分别为常数和时间的非随机函数的条件下讨论了有交易成本的上限型买权的定价问题.     

关于CIR模型中即期利率的条件密度及贴现债券定价(英文)

本文对CIR模型运用Kolgomorov向后方程给出即期利率的条件密度所满足的偏微分方程 ,并用谱方法将该密度表达成一个Laguerre型的正交级数之和 ,借助一个经验级数和公式 ,我们得出了该和式的第一类修正贝塞尔函数表达式 .同时 ,我们猜测贴现债券价格关于即期利率的特殊表达式 ,并通过求解两个一阶常微分方程验证了我们的猜测 .在文章的结尾 ,我们给出了贴现债券价格的条件期望和方差以反映必要的矩信息 .     

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.     

On the distribution tail of an integrated risk model: A numerical approach

We consider an insurance risk process with the possibility to invest the capital reserve into a portfolio consisting of a risky asset and a riskless asset. The stock price is modelled by an exponential Lévy process and the riskless interest rate is assumed to be constant. We aim at the risk assessment of the integrated risk process in terms of a high quantile or the far out distribution tail. We indicate an application to an optimal investment strategy of an insurer.     

认股权证的修正精算定价研究

基于修正Bladt和Rydberg在无市场假设下关于期权定价的保险精算方法的基础上,从评估实际损失和相应概率分布角度,利用公平保费原则建立认股权证的定价模型,并给出定价公式.且当投资者对原生资产期望回报率为无风险利率时,该定价为风险中性价格.     

Numerical solution of European call option with dividends and variable volatility

In this paper, the effect of strike price, interest rate, dividends and maturities on European call option with dividends is discussed. The volatility for the data of ONGC Ltd. listed in National Stock Exchange, India, during 03-01-2000 to 30-03-2009 is forecasted by GJR-GARCH method. The option price and Greeks are determined by solving modified Black-Scholes partial differential equation by adjusting forecasted volatility at each grid point of finite difference method. It is observed that call option premium decreases as strike price and dividend increases but it increases as rate of interest and time of maturities increases. Hence call option is more profitable for a long maturity, high interest rate and low dividend.     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

Monte Carlo analysis of convertible bonds with reset clauses

This paper analyzes some features of non-callable convertible bonds with reset clauses via both analytic and Monte Carlo simulation approaches. Assume that the underlying stock receives no dividends and that it has credit risk of the issuer. We mean by reset that the conversion price is adjusted downwards if the underlying stock price does not exceed pre-specified prices. Reset convertibles are usually issued when the outlook for the issuer is unfavorable. The price of any convertible bonds can be approximately viewed as a sum of values of an otherwise identical non-convertible bond plus an embedded option to convert the bond into the underlying stock. In this paper, we first develop an exact formula for the conversion option value of the European riskless convertible in the classical Black–Scholes–Merton framework. It is shown by Monte Carlo simulation that conversion option value estimates of the American risky convertible are located in a certain region defined by this formula. From estimates of the conversion probability, it is also shown that there exists an optimal reset time in the latter half of the trading interval.     

An optimal investment and consumption model with stochastic returns

We consider a financial market consisting of a risky asset and a riskless one, with a constant or random investment horizon. The interest rate from the riskless asset is constant, but the relative return rate from the risky asset is stochastic with an unknown parameter in its distribution. Following the Bayesian approach, the optimal investment and consumption problem is formulated as a Markov decision process. We incorporate the concept of risk aversion into the model and characterize the optimal strategies for both the power and logarithmic utility functions with a constant relative risk aversion (CRRA). Numerical examples are provided that support the intuition that a higher proportion of investment should be allocated to the risky asset if the mean return rate on the risky asset is higher or the risky asset return rate is less volatile. Copyright © 2008 John Wiley & Sons, Ltd.