决策依赖不确定条件下基于复合实物期权估值的工程系统投资决策研究

不确定性是复杂工程系统的内在属性,在决策依赖不确定条件下对工程系统的投资决策需考虑不确定性与决策过程之间的交互作用,使得投资决策问题的求解非常困难.提出了决策依赖不确定条件下复合实物期权估值的最小二乘模拟算法,方法较好地解决了在决策依赖不确定条件下由于不同期权价值相互耦合所带来的计算复杂性,进一步拓展了最小二乘模拟算法在期权估值中的应用,基于该方法,可以比较方便地解决决策依赖不确定条件下工程系统投资决策问题.     

不确定性、实物期权与企业价值—基于简约Schwartz-Moon模型的分析

将实物期权理论引入传统现金流量折现法的应用框架,在不确定性条件下运用实物期权定价法来评估企业价值,提出了简约的Schwartz-Moon(2001)实物期权定价模型,并在此基础上运用蒙特卡罗模拟方法来计算了百度公司的价值.     

基于改进无迹卡尔曼滤波的波动率研究

波动率估计是金融学的核心,波动几乎渗透金融市场的每一个领域.为了快速而精确地提取波动率,文章将比例UT变换与最小偏度单行采样技术和无迹卡尔曼滤波(UKF)算法相结合,提出一种适用于非线性高斯状态空间模型的改进的无迹卡尔曼滤波(MUKF)算法,并将该算法应用到扩散的期权定价模型中.最后通过对Heston随机波动模型进行模拟研究,发现在同时使用股票价格数据和期权数据时,可以精确地提取波动率,而且MUKF算法比UKF算法的计算时间更短.文章也对Heston模型中的波动率的波动参数进行了研究,研究发现MUKF算法可以准确地捕捉这种波动率特性.     

采购方主导的基于能力期权契约的应急物资采购模型

设计了一个基于能力期权契约的应急物资采购模型,政府作为唯一的采购方期初向一个合约供应商采购实物储备量,并向供应商购买一定量的生产能力期权,一旦在期权执行期内有应急物资需求发生,可立即将供应商储备的生产能力转化为实物产品.通过推导和算例模拟证明,这样的采购机制在大量减少政府应急物资实物储备量的同时,降低了政府的缺货风险.同时,也合理补偿了灾后供应商被安排突击生产应急物资发生的成本,应急物资供应链实现了协调,供和需双方实现了双赢.     

基于贝叶斯MCMC算法的美式期权定价

鉴于美式期权的定价具有后向迭代搜索特征,本文结合Longstaff和Schwartz提出的美式期权定价的最小二乘模拟方法,研究基于马尔科夫链蒙特卡洛算法对回归方程系数的估计,实现对美式期权的双重模拟定价.通过对无红利美式看跌股票期权定价进行大量实证模拟,从期权价值定价误差等方面同著名的最小二乘蒙特卡洛模拟方法进行对比分析,结果表明基于MCMC回归算法给出的美式期权定价具有更高的精确度.模拟实证结果表明本文提出的对美式期权定价方法具有较好的可行性、有效性与广泛的适用性.该方法的不足之处就是类似于一般的蒙特卡洛方法,会使得求解的计算量有所加大.     

不确定性投资决策中的期权博弈分析

本文应用期权博弈理论方法分析了存在竞争条件下的不确定性投资决策问题.建立了一个对称双寡头模型,用实物期权方法计算了模型中的领先者、跟随者和同时投资者的价值函数和投资临界点.     

线性规划问题的符号计算

应用各种符号计算系统可以很方便地求解各种线性代数问题,利用初等变换即可得到问题的精确解而不必预先编写程序,本文通过例子,根据单纯形算法原理,详细介绍了使用muMATH系统直接求解线性规划问题精确解的运算方法,人工变量所对应的列向量始终不参加运算,从而可大量节省存储量和计算量。     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

基于机制转换模型的碳排放权期权定价

机制转换模型可以将外部环境的变化迅速反映到对模型参数的调整中,故运用马氏链刻画外部机制建立机制转换模型,基于此进行碳排放权期权定价。为实现其价值函数的数值计算,首次设计并证明了一套倒向递归算法,该算法依据马氏链跳跃的划分实现递归,从而克服了马氏链带来的运算高复杂度,其数值结果展示了完整的波动率微笑和期限结构。最后通过与前人提出的算法以及蒙特卡洛模拟比较表明,倒向递归算法可获得更高的准确性和运算效率。     

基于择券和择时的国债期货定价

文章研究了基于择券和择时的国债期货定价问题,提出了在随机利率模型下,同时量化"择券期权"和"择时期权"的算法.通过对2015年至2017年中国国债期货市场进行实证研究,发现该算法对市值拟合度较高,并为敏感性因子计算和风险管理提供有力的支持.此外文章还分析了市场利率环境发生变化时"择券期权"和"择时期权"的特点,发现极端利率环境下,需要对"期权"价值重点关注.     

A semi-analytical method for VaR and credit exposure analysis

In this paper, we discuss new analytical methods for computing Value-at-Risk (VaR) and a credit exposure profile. Using a Monte Carlo simulation approach as a benchmark, we find that the analytical methods are more accurate than RiskMetrics delta VaR, and are more efficient than Monte Carlo, for the case of fixed income securities. However the accuracy of the method deteriorates when applied to a portfolio of barrier options.     

上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟

上证50ETF期权作为中国资本市场上股票期权的第一个试点产品,其定价问题尤为重要。本文分别运用B-S-M期权定价模型和蒙特卡罗模拟方法对其定价进行实证研究,分析结果表明:1)IGARCH模型比传统的GARCH模型更能较好地拟合上证50ETF的波动率;2)当模拟次数为1000时,蒙特卡罗方法的效率一致地高于B-S-M模型,并且除了对偶变量技术的拟蒙特卡罗其他模型的精确度也都高于B-S-M模型;3)B-S-M模型和蒙特卡罗模拟方法都可以较为准确地、有效地模拟出上证50ETF期权价格。这些研究将为今后期权定价模型的发展和完善提供必要的参考和指引。     

Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Lévy Processes

Lévy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper shows how to correct for this bias for a range of options by generating a sample from the extremes distribution of the Lévy process on subintervals. The method uses variance‐gamma and normal inverse Gaussian processes. The method gives considerable reductions in bias, so that it becomes feasible to apply variance reduction methods. The method seems to be a very fruitful approach in a framework in which many options do not have analytical solutions.     

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

Partition Weighted Approach For Estimating the Marginal Posterior Density With Applications

The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not available in many applications. We develop the partition weighted marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single Markov chain Monte Carlo output from the joint posterior distribution and the known unnormalized posterior density. The theoretical properties and various applications of the PWMDE are examined in detail. The PWMDE method is also extended to the estimation of conditional posterior densities. We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively. Supplementary materials for this article are available online.     

资产跳跃下CM策略多期收入保证价格模拟

恒定混合策略(CM策略)多期收入保证价格是保本基金发行方采取设置止损的CM\linebreak策略作为投资策略时收取保 本费的理论依据, 其中标的资产由复合泊松过程和维纳过程共同驱动, 这一定价问题内嵌奇异期权, 蒙特卡罗模拟方法擅长处理这种高维数量金融问题. 基于风险中性测度推导出多期收入保证价格的现值表达式, 用条件蒙特卡罗推导出这一现值表达式的模拟公式. 在给定参数下分别用普通蒙特卡罗和条件蒙特卡罗计算CM策略多期收入保证价格的数值解, 结果显示两种蒙特卡罗方法均能有效计算其数值解, 之后通过给定显著性水平下的置信区间长度评价两种方法的精确度, 结果显示条件蒙特卡罗比普通蒙特卡罗有很大改进. 接着运用条件蒙特卡罗模拟研究多期收入保证价格对不同参数范围的变化情况.     

Prices and sensitivities of Asian options: A survey

Asian options are hard to price both analytically and numerically. Even though they have been the focus of much attention in recent years, there is no single technique which is widely accepted to price Asian options for all choices of market parameters. For hedging purposes, the estimation of the price sensitivities is often as important as the evaluation of the prices themselves. This paper provides a survey of current methods for pricing Asian options and computing their sensitivities to the key input parameters. The methods discussed include: Monte Carlo simulation, the finite difference approach and various quasi analytical approaches and approximations. We discuss practical numerical issues that arise in implementing these methods. The paper compares the accuracy and efficiency of the different approaches and offers some general conclusions.     

金融中的Levy模型及其仿真

近20年来,金融中Levy模型与蒙特卡洛仿真技术日益受到重视. 在连续时间过程的金融建模中带跳跃的Levy模型相比于连续轨道的布朗运动模型能很好地刻画市场的跳跃,更好地拟合金融数据的统计特征,更准确地对衍生品定价. 但是,相较于经典的Black-Scholes模型,用Levy模型对衍生品定价以及求解对冲策略的计算复杂度大大增加. 蒙特卡洛仿真成为Levy模型计算中最重要的方法之一. 首先详细地介绍了Levy模型引入的背景,并引出仿真方法在其中重要的应用价值. 最后,简要地给出了Levy过程仿真及其梯度估计的基本方法.