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1.
随机利率下奇异期权的定价公式   总被引:1,自引:0,他引:1  
李淑锦  李胜宏 《数学学报》2008,51(2):299-310
在随机利率条件下,借助于测度变换获得了复合看涨期权的一般的定价公式,同时利用鞅理论和Girsanov定理,在利率服从于扩展的Vasicek利率模型时,得到了复合看涨期权精确的定价公式.用同样的方法,考虑了预设日期的重置看涨期权的定价问题,在利率服从同样的利率模型时,获得了重置看涨期权的定价公式.数值化的结果进一步说明了当利率遵循扩展的Vasicek利率模型时,B-S看涨期权的价格关于标的资产的价格是严格单调递增的,复合看涨期权的Geske公式是可以推广到随机利率的情况.  相似文献   

2.
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.  相似文献   

3.
分数跳-扩散模型下的互换期权定价   总被引:1,自引:0,他引:1  
何传江  方知 《经济数学》2009,26(2):23-29
用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了一类多资产期权——欧式交换期权的定价公式.该公式是标准跳扩散模型下的欧式期权及欧式交换期权定价公式的推广.  相似文献   

4.
Black-Scholes期权定价公式推广   总被引:11,自引:0,他引:11  
在Black-Scholes期权定价模型的基础上,进一步考虑标的资产受多个跳跃源影响的情况,用含有多维Poisson过程的Ito-Skorohod随机微分方程描述标的资产价格的动态运动,应用等价鞅测度变换方法导出一般形式的欧式期权定价公式,并讨论了利率,波动率不是常数情况下的拓广形式.  相似文献   

5.
考虑到标的资产(股票)价格和利率的随机性及均值回复特征,采用Hull-White模型刻画利率的变化规律,指数Ornstein-Uhlenbeck(O-U)过程刻画有红利支付的股票价格变化.利用计价单位转换的方法研究了基于以上模型且有连续支付红利情况下的一类幂型欧式期权定价问题,并得到了其定价公式.  相似文献   

6.
实物期权的定价在风险投资决策过程中具有重要意义.传统的实物期权定价方法忽略标的资产价值和投资成本的模糊性,从而可能导致错误的投资决策.本文主要研究了具有模糊标的的资产价值和投资成本情形时的实物期权定价模型.文中将这些模糊因素分别视为模糊数和模糊变量,然后运用模糊集合论,结合B-S期权定价理论,对实物期权进行定价,得到了基于模糊集合论的实物期权定价模型.  相似文献   

7.
主要探讨不确定环境下用模糊集理论处理亚式期权的定价问题.运用梯形模糊数来表示标的资产价格、无风险利率、红利率和波动率,建立了亚式期权的加权可能性均值模糊定价模型,得到连续几何和算术亚式期权的模糊价格公式.最后通过数值例子表明:亚式期权的加权可能性均值模糊定价模型具有很大的灵活性,更符合现实的不确定情况,具有较强的实用价值.  相似文献   

8.
假设利率服从扩展的Vasicek模型,标的资产价格服从分数跳-扩散过程,利用无套利理论与多元正态分布,导出了规定时间的重置期权的定价公式.  相似文献   

9.
分数布朗运动环境中欧式未定权益的定价   总被引:23,自引:0,他引:23  
本文在标的资产价格服从几何分数布朗运动模型假设下,求出了在标的资产有红利支付时的欧式未定权益的一般定价公式及几种奇异期权的定价公式。  相似文献   

10.
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.  相似文献   

11.
用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了欧式复合期权的定价公式.结果推广了Gukhal以及Li等关于传统跳-扩散模型下的欧式复合期权的定价公式.  相似文献   

12.
Asian options represent an important subclass of the path-dependent contracts that are identified by payoff depending on the average of the underlying asset prices over the prespecified period of option lifetime. Commonly, this average is observed at discrete dates, and also, early exercise features can be admitted. As a result, analytical pricing formulae are not always available. Therefore, some form of a numerical approximation is essential for efficient option valuation. In this paper, we study a PDE model for pricing discretely observed arithmetic Asian options with fixed as well as floating strike for both European and American exercise features. The pricing equation for such options is similar to the Black-Scholes equation with 1 underlying asset, and the corresponding average appears only in the jump conditions across the sampling dates. The objective of the paper is to present the comprehensive methodological concept that forms and improves the valuation process. We employ a robust numerical procedure based on the discontinuous Galerkin approach arising from the piecewise polynomial generally discontinuous approximations. This technique enables a simple treatment of discrete sampling by incorporation of jump conditions at each monitoring date. Moreover, an American early exercise constraint is directly handled as an additional nonlinear source term in the pricing equation. The proposed solving procedure is accompanied by an empirical study with practical results compared to reference values.  相似文献   

13.
假定标的股票服从分数次布朗运动,应用偏微分方程的方法求出下降敲出欧式看涨障碍期权价格显示解,以及看涨-看跌的平价关系式.最后,通过有限差分法比较了显示解的准确性,分析了Hurst参数对期权价格和风险特征参数的影响.  相似文献   

14.
国内外利率为随机的双币种重置型期权定价   总被引:1,自引:0,他引:1  
黄国安  邓国和 《大学数学》2011,27(2):125-132
双币种重置期权的特征是指在终端期T时的收益依赖于预先设定的t<,0>时刻标的资产的价格与执行价K>0(事先给定)的大小关系重新设置期权的执行价从而给出其定价,这种期权是投资于外国资产的一种合约,其风险不仅依赖外国资产价格的变化,还受外国货币的汇率以及国内外两种利率波动的影响,所以在实际应用方面十分广泛.本文首先就标的资...  相似文献   

15.
Abstract

We consider the pricing of options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump-diffusion model. We suppose that the market interest rate, the drift and the volatility of the underlying risky asset switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The measure process is defined to be a generalized mixture of Poisson random measure and encompasses a general class of processes, for example, a generalized gamma process, which includes the weighted gamma process and the inverse Gaussian process. Another interesting feature of the measure process is that jump times and jump sizes can be correlated in general. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the underlying risky asset. We employ the generalized regime-switching Esscher transform to determine an equivalent martingale measure in the incomplete market setting. A system of coupled partial-differential-integral equations satisfied by the European option prices is derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Simulation results of the model have been presented and discussed.  相似文献   

16.
假定标的股票服从分数布朗运动,应用二次近似法和偏微分方程方法求出了美式下降敲出看涨、看跌障碍期权价格近似解以及最佳实施边界.最后,通过显式差分法比较近似解的准确性,并分析Hurst参数对期权价格和最佳实施边界S*的影响.  相似文献   

17.
Finding semiparametric bounds for option prices is a widely studied pricing technique. We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic (Collar and Gap) call options given mean and variance information on the underlying asset price. Mathematically, we extended domination technique by quadratic functions to bound mean and variances. This work was supported by National Science Foundation of the United States (Grant Nos. DMS-0720977 and DMS-0805929)  相似文献   

18.
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.  相似文献   

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