欧式幂期权定价中隐含标准差的统计特征

首先将欧式看涨幂期权定价公式展成Taylor级数,得到幂期权的近似无偏估计.然后通过蒙特卡罗方法进行实验,从幂期权近似估计的分布中推出隐含标准差的分布特征.并改变期权中幂的值或执行价格的值,得到隐含标准差的期望和方差等统计特征.     

欧式向下敲出看涨幂期权的Esscher变换定价

首先根据障碍期权的不同类型,对普通欧式向下敲出看涨幂期权、部分时间开始、部分时间结束、一般部分时间欧式向下敲出看涨幂期权给出定义.通过E sscher变换分别给出定价公式.另外,对两资产欧式向下敲出幂期权也给出了定价公式,为实践者提供了理论上的参考价格.最后,阐述了此方法的优点.     

幂型支付的欧式期权定价公式

在等价鞅测度框架下,讨论了(在到期时刻)期权处于实值状态时支付函数为幂型的股票欧式期权定价公式.这里我们假设无风险利率,股票预期收益率和股价波动率都是时间的确定性函数.本文结果不但包含了原始的Black-Scholes公式,而且可用于上封顶与下保底(幂型)欧式看涨期权的定价.     

分数跳-扩散环境下几种新型期权定价模型

假定股票价格遵循分数跳-扩散过程,利用公平保费原则和价格过程的实际测度,获得几种新型期权——欧式看涨幂期权、欧式上封顶及下保底看涨幂期权定价公式.对期权定价模型进行了推广.     

随机波动率跳跃扩散模型下复合期权定价

复合期权是一类以期权作为标的物的奇异型合约,它已广泛应用于许多金融实践。本文在股价满足一类随机波动率及跳跃均存在于股价和波动率的仿射跳跃扩散模型下(也称随机波动率混合跳跃扩散模型)考察了复合期权的定价。应用二维特征函数和Fourier反变换方法获到了标的为欧式标准看涨期权的欧式复合看涨期权的定价半封闭公式,并将其应用于推导扩展期权的定价。最后,借助于离散快速Fourier变换法(FFT)数值计算定价公式,并用数值实例分析了期权价格对波动率的敏感性。数值结果表明扩散波动和跳跃波动对期权价格都有正的影响,而且跳跃波动的冲击非常显著。     

标的资产价格服从分数布朗运动的几种新型期权定价

在等价鞅测度下,研究标的资产价格服从分数布朗运动的几种新型股票期权定价公式——n次幂期权、(幂型)上封顶及下保底型欧式看涨期权.并与基于标准布朗运动的期权定价公式进行比较分析,进一步论证布朗运动只是分数布朗运动的一种特例,可基于分数布朗运动对原有的期权定价模型进行推广.     

随机利率Vasicek模型下的欧式缺口期权的定价研究

研究随机利率Vasicek模型下欧式缺口期权的定价问题,利用偏微分方程方法给出了欧式缺口看涨期权和看跌期权的定价公式,并且是Vasicek利率模型下标准欧式期权定价公式的一种推广.     

汇率连动欧式幂型期权鞅定价及避险

研究了汇率连动选择权中执行价是本国货币的外国股票权证的欧式幂型期权的鞅定价问题,推导了其看涨、看跌定价公式,并求出了其相应的避险参数.     

随机利率下服从分数O-U过程的欧式幂期权定价

该文考虑了利率和标的资产价格的随机性和均值回复行为,把扩展的Vasick模型和分数O-U过程进行组合,在随机利率环境下,研究了标的资产价格服从分数O-U过程的两类欧式幂期权定价问题,得到相应的定价公式,并给出了欧式幂期权的看涨.看跌平价关系.     

分数维Vasicek利率模型下的欧式期权定价公式

假定股票价格和利率的运动过程服从几何分数维布朗运动,利用风险对冲技术,分数维布朗运动随机分析理论与偏微分方程方法,得到了分数维Vasicek随机利率下欧式期权所满足的定价方程,获得了波动率是对间函数的情形下欧式看涨和看跌期权的一般定价公式以及它们的平价公式.     

Two extensions to barrier option valuation

We first present a brief but essentially complete survey of the literature on barrier option pricing. We then present two extensions of European up-and-out call option valuation. The first allows for an initial protection period during which the option cannot be knocked out. The second considers an option which is only knocked out if a second asset touches an upper barrier. Closed form solutions, detailed derivations, and the economic rationale for both types of options are provided.     

Approximate valuation of average options

This paper concerns the valuation of average options of European type where an investor has the right to buy the average of an asset price process over some time interval, as the terminal price, at a prespecified exercise price. A discrete model is first constructed and a recurrence formula is derived for the exact price of the discrete average call option. For the continuous average call option price, we derive some approximations and theoretical upper and lower bounds. These approximations are shown to be very accurate for at-the-money and in-the-money cases compared to the simulation results. The theoretical bounds can be used to provide useful information in pricing average options.     

二次式变异期权的定价模型

本讨论了一种变异期权-收益结构为二次式的欧式买入期权定价问题。在股票价格服从几何布朗运动的行为模型下，推导出收益结构为二次式的欧式买入期权的定价公式。     

The pricing of options on an interval binomial tree. An application to the DAX-index option market

This paper implements a model setup in Muzzioli and Torricelli [Int. J. Intell. Syst. 17 (6) (2002) 577–594] for deriving implied trees and pricing options when the put–call parity is not fulfilled. The model basically extends Derman and Kani’s [Risk 7 (2) (1994) 32–39], whereby call (put) prices are also used in the lower (upper) part of the tree thus exploiting the information content of both call and put prices. The DAX-index option market is chosen for this application because it is a relatively new European market where short-selling restrictions may induce put–call parity violations and the nature of the option (European) and of the underlying (dividends reinvested in the index) avoid some estimation problems. In order to test the pricing fit of the model, a non-linear optimisation procedure is proposed to estimate a unique implied tree which allows a comparison between the model prices, Derman and Kani’s and market prices. The results suggest that the MT model improves the pricing.     

基于跳-分形模型的美式看涨期权定价

假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.     

汇率连动期权的保险精算定价

利用保险精算方法给出了汇率连动期权的定价公式,获得了欧式看涨期权和看跌期权价格的表达式及平价关系。     

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.     

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.