中国股市期权波动率微笑特征的实证分析

波动率微笑现象显示了期权隐含波动率和执行价格之间的关系.在理想的完全符合Black-Scholes期权定价模型假设的情况下,期权隐含波动率关于执行价格应该是一条水平线.然而,在实证分析中,对隐含波动率和执行价格进行拟合并绘制曲线,会产生一个倾斜或微笑形状的曲线,证明Black-Scholes期权定价模型存在一定的缺陷.本文从Black-Scholes期权定价模型和回归分析出发,尝试用不同的函数形式(对数函数、二次函数和三角函数)拟合波动率的解析表达式并绘制图形,最终以调整的可决系数最大为最优.首先拟合截面数据,对一固定的时间期限拟合出波动率关于执行价格的解析表达式以及波动率微笑曲线,然后将不同时间期限的波动率微笑曲线排列成时间序列,拟合面板数据,即波动率微笑曲面.然而由于面板数据的复杂性,该模型的拟合优度相对于截面数据有所降低,但是在考虑了期限与执行价格对隐含波动率的交互影响后,面板数据模型调整的可决系数显著增大,拟合优度得到提高.     

一种无风险利率时变条件下的Black-Scholes期权定价模型

本文研究了无风险利率改进的Black-Scholes期权定价模型问题.利用指数函数和Ito公式的方法,获得了一种改进的Black-Scholes期权定价模型,推广了现有Black-Scholes期权定价模型的结果.     

基于外汇汇率的期权定价及其实证分析

在外汇汇率服从连续扩散过程模型下,研究了外汇汇率的几何平均亚式期权和附有汇率范围的示性函数的新型幂期权定价问题。在实证分析中,通过美元/人民币汇率的真实数据来计算以上所研究期权的价格,并和Black-Scholes模型下的期权定价进行比较,同时对相关期权的隐含波动率进行了分析。     

时间分数阶期权定价模型的一类有效差分方法

时间分数阶期权定价模型(时间分数阶Black-Scholes方程)数值解法的研究具有重要的理论意义和实际应用价值.对时间分数阶Black-Scholes方程构造了显-隐格式和隐-显差分格式,讨论了两类格式解的存在唯一性,稳定性和收敛性.理论分析证实,显-隐格式和隐-显格式均为无条件稳定和收敛的,两种格式具有相同的计算量.数值试验表明:显-隐和隐-显格式的计算精度与经典Crank-Nicolson(C-N)格式的计算精度相当,其计算效率(计算时间)比C-N格式提高30%.数值试验验证了理论分析,表明本文的显-隐和隐-显差分方法对求解时间分数阶期权定价模型是高效的,证实了时间分数阶Black-Scholes方程更符合实际金融市场.     

企业经营者股票期权薪酬机制的模型探讨

采用 Black-Scholes期权定价理论 ,建立了激励机制下企业经营者股票期权薪酬机制的分析、操作模型     

简单可转换债券的定价——一种鞅方法

可转换债券作为债券和期权的混合体,其定价比债券和期权的定价都要复杂.本文用鞅方法讨论可转换债券的定价问题,给出了便于计算的类似于Black-Scholes模型的定价公式.但我们利用鞅方法使定价模型的推导更自然.基于这一定价模型,可转换债券的价格可分解为转换期权的价格和简单债券的价值之和.     

美式看跌期权定价的两种有限差分格式

基于Black-Scholes模型,采用指数拟合有限差分法与外推的指数拟合有限差分法对美式看跌期权价值进行了数值计算,对这两种数值方法及其与已往的显式、隐式、C-N等有限差分的优缺点进行了比较,并给出数值算例,通过对此算例做的一系列数值试验,验证了算法的有效性,并得到了一些在期权交易的实际操作中有用的结果.     

基于实物期权定价方法的林业碳汇项目投资决策仿真研究

文章针对林业碳汇项目投资决策的复杂性、动态性和不确定性过程,利用林业—碳汇共同经营决策模型计算林业碳汇项目在投资期内的期望价值,采用实物期权定价方法对不同阶段不同策略下的林业碳汇项目价值进行评估,同时提出了多主体仿真建模方法,利用NetLogo仿真软件对林业碳汇项目投资决策过程进行动态模拟。仿真系统中涉及到的主体有林地、CO₂和投资者,投资者主要是作为观察者的身份,在不同阶段会做出不同的投资策略。模拟仿真三种不同状态下投资者的决策变化:一是传统林业投资动态模拟,不包含碳汇和期权因素动态模拟;二是引入碳汇市场后的林业投资动态模拟;三是引入碳汇市场和期权后林业投资动态模拟。NetLogo仿真分析结果表明引入碳汇市场可以提高投资者的收益并改变投资者的经营策略,同时引入期权,不仅增加了投资者的积极性而进行扩张投资,还可以更好地发挥林木碳汇功能,体现林业的生态价值及经济价值。     

混合分数布朗运动环境下短期利率服从vasicek模型的欧式期权定价

本文研究了混合分数布朗运动环境下欧式期权定价问题.运用混合分数布朗运动的Ito公式,得到了Black-Scholes偏微分方程.同时,通过求解Black-Scholes方程,得到了欧式看涨、看跌期权的定价公式。推广了Black-Scholes模型有关欧式期权定价的结论.     

分数布朗运动驱动的幂型期权定价模型研究

股价运动分形特征的发现,说明布朗运动作为期权定价模型的初始假定存在缺陷.本文假定标的资产价格服从几何分数布朗运动,利用分数风险中性测度下的拟鞅(quasi-martingale)定价方法重新求解分数Black-Scholes模型,进而对幂型期权进行定价.结果表明,幂型期权结果包含了Black-Scholes公式和平方期权结果,且相比标准期权价格,分数期权价格要同时取决于到期日和Hurst参数H.     

中国钢铁业上市公司并购中盈余管理研究—基于效率视角

本文通过改进度量盈余管理程度的Yoon-miller模型,测算2003-2009年中国钢铁业上市公司并购前后的可操纵性利润和全要素生产率,并对并购中盈余管理与效率的内在关系进行分析。结果表明:并购后一年全要素生产率有效的钢铁上市公司在并购当年存在向上的盈余管理,并购后一年及并购当年全要素生产率均有效的钢铁上市公司,在并购后一年容易进行较大幅度的向下盈余管理行为。     

离散条件下标的资产带跳的德尔塔对冲误差研究

讨论了离散条件下的德尔塔对冲以及含泊松跳跃的布莱克—休斯模型下期权的定价问题.在布莱克—休斯模型中对冲被假设为连续发生的,当应用于离散的交易时,对冲误差就产生了.考虑到对冲误差,得出一种离散条件下标的资产带泊松跳跃的修正的布莱克—休斯方程和依赖再对冲区间长度的更精确的德尔塔值.     

Lie-algebraic approach for pricing moving barrier options with time-dependent parameters

In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.     

Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.     

基于GARCH模型考虑股本稀释作用的权证定价

考虑到认购权证对股本有稀释作用,把对认购权证定价转化为一个看涨期权的定价,运用GARCH模型得出看涨期权标的资产波动率的近似经验分布,根据期权定价的Black-Scholes公式,得出认购权证价格的近似分布.     

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.     

Analytic models for parameter dependency in option price modelling

Options are a type of financial instrument classed as derivatives, as they derive their value from an underlying asset. The equations used to model the option price are often expressed as partial differential equations (PDEs). Once expressed in this form, a discretization method on a finite grid can be applied and the numerical valuation obtained. Remains the problem of writing down an (approximate) closed-form analytic model for the option price in function of all the variables and parameters, which is the main objective of this paper. At the same time we also consider the Greeks, which are the quantities representing the sensitivities of the price to a change in the underlying variables or parameters. Discrete values for these Greeks can again be derived, either directly from the differentiation matrices occurring in the option price PDE or by solving new but similar PDEs. Next, analytic models for the Greeks are computed in the same way as for the option price. As a prototype case, The Black-Scholes PDE for European call options is considered.     

Optimal stopping, free boundary, and American option in a jump-diffusion model

This paper considers the American put option valuation in a jump-diffusion model and relates this optimal-stopping problem to a parabolic integro-differential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its counterpart European price and the early exercise premium. Compared with the Black-Scholes (BS) [5] model, this premium has an additional term due to the presence of jumps. We prove the continuity of the free boundary and also give one estimate near maturity, generalizing a recent result of Barleset al. [3] for the BS model. Finally, we study the effect of the market price of jump risk and the intensity of jumps on the American put option price and its critical stock price.     

Calibration of a basket option model applied to company valuation

Applying real options thinking to company valuation seems theoretically and intuitively appealing. However, the real option analogy of a single European option as well as the compound option proxy perform poorly when applied to company valuation. We therefore suggest to rework the building blocks of real option applications to corporate valuation.  We introduce a framework to delineate the distribution of the underlying asset in the risk neutral world, which is important in order to value any derivative. This is achieved by an algorithm to calibrate a basket option model using real world data of observed share prices. The fitting takes account of the class of stable distributions. The index of stability of asymmetric α stable distribution serves as an over-all parameter to characterise the specific distribution.     

Numerical methods for backward Markov chain driven Black-Scholes option pricing

The drift, the risk-free interest rate, and the volatility change over time horizon in realistic financial world. These frustrations break the necessary assumptions in the Black-Scholes model (BSM) in which all parameters are assumed to be constant. To better model the real markets, a modified BSM is proposed for numerically evaluating options price-changeable parameters are allowed through the backward Markov regime switching. The method of fundamental solutions (MFS) is applied to solve the modified model and price a given option. A series of numerical simulations are provided to illustrate the effect of the changing market on option pricing.