模糊环境下美式看跌期权的定价研究

应用模糊集理论将无风险利率和波动率进行模糊化,以梯形模糊数替代精确值,将美式期权的定价模型扩展到美式期权模糊定价模型.得到了模糊风险中性概率表达式,并在此概率测度下推导出多期二叉树模糊定价模型,以及二叉树上各节点以梯形模糊数表示的模糊期权价值,以数值模拟演示了美式看跌期权的模糊定价过程.最后分析了不同风险偏好投资者在不确定环境下的套利决策行为,结果表明风险偏好大的投资者具有较高的置信水平、较小的主观模糊期权价格以及较大的无风险套利区间.     

真实利率波动对长期资产配置的影响(英)

对于单期的投资者而言,无违约风险的固定收益证券被视为无风险资产.这是因为固定收益证券的收益率在投资的初期就能确定.然而在考虑长期的投资时,投资者可以调整资产配置,固定收益证券也将面临再投资的利率波动风险,因此不能再被视为无风险资产.本文在一类特殊的``习惯形成"效用函数的框架下讨论长期资产配置.在一系列为简化问题而作的假设之下,本文推导出了真实利率波动对风险资产配置权重的影响,并且为计算实际长期资产配置的最优比例提供了理论依据和算法.     

真实利率波动对长期资产配置的影响(英文)

对于单期的投资者而言,无违约风险的固定收益证券被视为无风险资产.这是因为固定收益证券的收益率在投资的初期就能确定.然而在考虑长期的投资时,投资者可以调整资产配置,固定收益证券也将面临再投资的利率波动风险,因此不能再被视为无风险资产.本文在一类特殊的"习惯形成"效用函数的框架下讨论长期资产配置.在一系列为简化问题而作的假设之下,本文推导出了真实利率波动对风险资产配置权重的影响,并且为计算实际长期资产配置的最优比例提供了理论依据和算法.     

管理人因素对风险项目期权估值的影响

本基于对风险项目及其“孪生证券”风险和收益特性的分析，认为真正的“孪生证券”实际中很难存在，进而提出利用“近似孪生证券”与无风险证券构造资产组合来复制实物期权收益特征，利用无风险套利分析确定项目实物期权价值的方法。但考虑到管理人因素造成的实物期权内部风险特征的不可复制性，本进一步提出利用“确定性等值”将内部风险价值V1具体化，从而实现对“近似孪生证券”方法进行修正。     

分数布朗环境下的实物期权与项目资本预算

在资本预算中,实物期权估值方法考虑了项目的经营柔性,提高了项目的预算价值。分数布朗环境下实物期权估值方法在标准布朗环境下实物期权的基础上考虑了标的资产价格运动的分形特征,其计算结果更符合现实情况。通过实证分析,表明了在存在管理柔性的前提下,估值结果更客观,符合市场特征,从而为项目的估值和经营决策提供一个新视角。     

次分数Vasicek随机利率模型下的欧式期权定价

本文对经典的B-S模型的假设条件进行放松,在假定利率为随机波动情况下对欧式期权定价进行讨论.作为利率的载体,本文首先对零息票债券进行定价,得出利率风险的市场价格的含义.其次,利用投资组合的?对冲原理构造无风险资产,求得欧式期权在次分数布朗运动驱动的随机利率模型下所满足的偏微分方程.最后,经过变量替换转化为经典的热传导方程,获得了欧式期权定价公式.     

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。     

连续支付红利及有交易成本的领子期权定价模型

在无风险利率r(t)和波动率σ(t)均为时间t的函数及市场无套利假设下,分别考虑了连续红利率q(t)和有交易成本情况下的领子期权定价,通过建立相应定价模型,得到了领子期权不同的定价公式.     

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.     

具有不同借贷利率的欧式未定权益定价模型

本文假定借款利率大于或等于无风险利率 ,并在股票的期望收益率、波动率和红利率都随时间变化情形下 ,建立较合理的金融市场模型。利用倒向随机微分方程及Feynman Kac公式 ,得到了欧式看涨和看跌期权买卖双方的价格公式以及套期保值策略 ,从而可看出借贷利率各自对期权价格的影响 .     

Generalised soft binomial American real option pricing model (fuzzy–stochastic approach)

The stochastic discrete binomial models and continuous models are usually applied in option valuation. Valuation of the real American options is solved usually by the numerical procedures. Therefore, binomial model is suitable approach for appraising the options of American type. However, there is not in several situations especially in real option methodology application at to disposal input data of required quality. Two aspects of input data uncertainty should be distinguished; risk (stochastic) and vagueness (fuzzy). Traditionally, input data are in a form of real (crisp) numbers or crisp-stochastic distribution function. Therefore, hybrid models, combination of risk and vagueness could be useful approach in option valuation. Generalised hybrid fuzzy–stochastic binomial American real option model under fuzzy numbers (T-numbers) and Decomposition principle is proposed and described. Input data (up index, down index, growth rate, initial underlying asset price, exercise price and risk-free rate) are in a form of fuzzy numbers and result, possibility-expected option value is also determined vaguely as a fuzzy set. Illustrative example of equity valuation as an American real call option is presented.     

CEV模型下家庭最优投资决策问题

考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Legendre-对偶变换进行求解,得到最优策略的显示解,并通过敏感性分析进行验证表明,家庭投资需求是弹性方差系数的减函数,解释了家庭流动性财富的增加对最优投资比例呈现边际效用递减趋势.     

随机利率下期权定价的探讨

利用Ho-Lee和Vasicek模型的简化形式推导出了Black-Scholes假设下的随机利率欧式期权定价公式,对无风险利率是常数的期权定价模型进行扩展,并与一般情况进行了分析与比较。     

Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.     

The American Foreign Exchange Option in Time-Dependent One-Dimensional Diffusion Model for Exchange Rate

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process. In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put option and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities. Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium. The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods.     

货币政策、非国有企业投资与R&D项目中的共享型复合实物期权价值预期

如何合理评估货币政策对R&D项目中的共享型复合实物期权价值的影响已成为非国有企业决策者面临的重要问题。本研究根据非国有企业决策者的认知偏差和分子动力学理论,在分析R&D项目中的实物期权特征及价值相互作用的基础上,构建了共享型复合实物期权价值预期模型,研究表明:当货币扩张程度增强时,项目价值预期增大;当货币扩张程度减弱时,项目价值预期减小。另外,货币扩张强度对期权价值的上、下限和预期值具有非线性影响;货币政策的变化范围对期权价值预期的解释程度不同;货币扩张系数与期权价值的上下限成正比,但与期权价值的预期值不完全成正比。最后通过仿真实验检验了该影响的变化机理和效果,从而为非国有企业决策者提供经验参考。     

混合分数布朗运动下欧式期权模糊定价研究

本文采用混合分数布朗运动来刻画标的股票价格的动态变化,以此体现金融市场的长记忆性特征。在混合分数Black-Scholes模型的基础上, 基于标的股票价格、无风险利率和波动率均是模糊数的假定下,构建了欧式期权模糊定价模型。其次,分析了金融市场长记忆性的度量指标 Hurst指数H对欧式期权模糊定价模型的影响。最后,数值实验表明:考虑长记忆性特征得到的欧式期权模糊定价模型更符合实际。