股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

基于分数布朗运动的具有信息影响的投资组合期权定价

假设标的资产价格服从分数布朗散运动,其价格跳跃度服从复合Poisson分布,采用拟鞅定价的方法,得到了具有信息影响的投资组合的期权定价公式.     

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??Model of option pricing driven by Brownian motion is the most classical model. However, it can not describe long-term property and invariance in a short period of time of asset price. In this article, option pricing model driven by sub-fractional Brownian motion is studied under time-transform with dividend-paying. Firstly, the model of diffusion B-S model of sub-fractional Brownian motion is build, and get option pricing formula with dividends. Secondly, statistical simulation is used by real data in finance and show that new model can reflect real financial assets.     

混合分数布朗运动下分离交易可转债的定价

在假定股票价格由混合分数布朗运动驱动,且市场利率服从Vasicek过程的条件下,建立了分离交易可转债定价的金融市场偏微分方程．通过求解偏微分方程、并利用无套利定价原理得到了分离交易可转债定价的显示解.     

Gaussian moving averages,semimartingales and option pricing

We provide a characterization of the Gaussian processes with stationary increments that can be represented as a moving average with respect to a two-sided Brownian motion. For such a process we give a necessary and sufficient condition to be a semimartingale with respect to the filtration generated by the two-sided Brownian motion. Furthermore, we show that this condition implies that the process is either of finite variation or a multiple of a Brownian motion with respect to an equivalent probability measure. As an application we discuss the problem of option pricing in financial models driven by Gaussian moving averages with stationary increments. In particular, we derive option prices in a regularized fractional version of the Black–Scholes model.     

标的资产服从几何分数布朗运动的期权定价

本文在M ogens B ladt和T ina H av iid R ydberg无市场假设,仅利用价格过程的实际概率的期权保险精算定价模型的基础上,得出了标的资产服从几何分数布朗运动的欧式期权定价公式,并说明了几何布朗运动是本文的一种特殊情况.     

分数布朗运动下几何平均亚式权证的定价

假设股票价格变化过程服从几何分数布朗运动,建立了分数布朗运动下的亚式期权定价模型.利用分数-It-公式,推导出分数布朗运动下亚式期权的价值所满足的含有三个变量偏微分方程.然后,引进适当的组合变量,将其定解问题转化为一个与路径无关的一维微分方程问题.进一步通过随机偏微分方程方法求解出分数布朗运动下亚式期权的定价公式.最后利用权证定价原理对稀释效用做出调整后,得到分数布朗运动下亚式股本权证定价公式.<正>~~     

混合分数布朗运动环境下欧式期权定价

假设股票价格变化过程服从混合分数布朗运动,建立了混合分数布朗环境下支付连续红利的欧式股票期权的定价模型.利用混合分数布朗运动的It-公式,将支付连续红利的欧式股票期权的定价问题转化为一个偏微分方程,通过偏微分方程求解获得了混合分数布朗运动环境下支付连续红利的欧式股票看涨期权的定价公式.     

Arbitrage and hedging in a non probabilistic framework

The paper studies the existence of arbitrage strategies in models without a semi-martingale structure. This is achieved by starting with a trajectory space that is treated as a topological space. Classes of admissible portfolios are then introduced providing arbitrage free market models in a trajectory based sense. Several examples, extending the trajectory classes of Brownian diffusion, fractional Brownian motion, weak Brownian motion and counting processes illustrate the new approach.     

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black–Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian motion does not adequately capture features of market equity returns. One popular alternative for modeling equity returns consists in replacing the geometric Brownian motion by an exponential of a Lévy process. In this paper we use this latter model to study variable annuity guaranteed benefits and to compute explicitly the distribution of certain exponential functionals.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It\^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment. According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

Pricing and hedging in a single period market with random interval valued assets

In this article, a new financial market model, in which securities have random interval valued payoffs, is proposed. As an extension of traditional random market model, some concepts, such as robust arbitrage opportunities, risk-neutral pricing measures and robust replicative strategies, are given and discussed parallel to those in traditional market analysis. With these new concepts, problems of pricing and hedging are analyzed. It is shown that the requirement of no robust arbitrage opportunities is equivalent to the existence of risk-neutral pricing measures. Taking no robust arbitrage as the valuation principle, the problem of pricing a contingent claim with random interval valued payoff is discussed. All no robust arbitrage prices of the claim form an interval, whose endpoints can be got from the risk-neutral pricing measures or from robust replicative strategies.     

分数跳-扩散运动下欧式复杂任选期权定价

本文假定股票价格过程服从分数跳一扩散运动,且期望收益率和波动率均为常数,在市场无套利的情形下,利用拟鞅定价的方法,得到了欧式复杂任选期权的解析定价公式．     

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。     

布朗运动和泊松过程共同驱动下的欧式期权定价

针对布朗运动和泊松过程共同驱动下股票价格的随机微分方程,利用It0公式和随机积分的方法,得到了该形式下欧式期权定价的模型,并给出了模型的求解.     

分数随机利率模型中的期权定价

本文研究分数随机利率模型中的期权定价问题.通过选取不同的资产作为计价单位及相应的测度交换,将经典模型中的测度变换方法推广到分数布朗运动市场环境,既丰富了分数期权定价的拟鞅方法,也得到了股票价格与利率分别服从几何分数布朗运动时的期权定价公式.     

基于鞅方法下分数布朗运动欧式回望期权的定价

利用分数布朗运动研究了一种强路径依赖型期权—回望期权的定价问题.首先列出了有关的定义和引理;其次利用该定义和引理建立了分数布朗运动情况下的价格模型,通过鞅方法,得到了回望期权价格所满足的方程;最后分别给出了看跌回望期权和看涨回望期权的定价公式的显式解.     

A note on first-passage times of continuously time-changed Brownian motion

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time scale. This equips the modelled returns with desirable stylized facts such as volatility clusters and jumps. For continuous time transformations, independent of the Brownian motion, we show that analytical results for the double-barrier problem can be obtained via the Laplace transform of the time change. The result is a very efficient power series representation for the resulting exit probabilities. We discuss possible specifications of the time change based on integrated intensities of shot-noise type and of basic affine process type.     

An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit

In this paper we explore an identity in distribution of hitting times of a finite variation process (integrated geometric Brownian motion) and a diffusion process (geometric Brownian motion with affine drift), both of which arise from various applications in financial mathematics. We develop semi-analytical solutions to fair charges of variable annuity guaranteed minimum withdrawal benefit from both a policyholder’s perspective and an insurer’s perspective. The pricing framework from the policyholder’s perspective was known previously in the literature only by numerical methods, whereas the insurer’s pricing method was used in the industry but only with Monte Carlo simulations. While comparing their similarities and differences, we prove under the assumption of no friction cost the two pricing approaches are equivalent. In the presence of friction cost, the semi-analytic solutions in this paper lead to a fast and accurate algorithm for determining rider charges and other management fees.     

不完全市场的保险定价研究

完全市场上的保险定价问题是人们比较熟悉的研究内容,但它不符合市场实际.本文在不完全市场上研究保险定价的问题.通过对累积保险损失的分析,建立在累积赌付下的保险定价模型;基于对一个无风险资产和有限多个风险资产的投资,建立保险投资定价模型.通过变形,得到相应的保险价格的倒向随机微分方程,并利用倒向随机微分方程的理论和方法,得到了相应的保险价格公式.最后,给出释例进行了分析.本文的研究,不用考虑死亡率、损失的概率分布等因素,为保险定价提供了新的思路,丰富了有限的保险定价方法.