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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. 相似文献
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研究了欧式幂期权定价公式中价格的渐近无偏估计和隐含波动率估计的统计特性。利用Chaudhury M.M(1989)提出的研究欧式期极定价公式中渐近无偏估计的方法以及隐含波动率求解方法,研究了两种欧式幂型看涨期权定价公式(欧式看涨期权的价值定义分别为m ax(STα-X,0)和m ax(STα-Xa,0)中的隐含波动率的估计的统计特征、幂函数的幂指数选取以及两种幂函数期权定价公式的优劣。Monte-Carlo统计计算的模拟结果说明。幂期权定价公式中幂指数α取值应为α>0,而且欧式看涨期权的价值定义为m ax(STα-Xα,0)更为合理。 相似文献
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幂型支付的欧式期权定价公式 总被引:16,自引:6,他引:10
陈万义 《数学的实践与认识》2005,35(6):52-55
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. 相似文献
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标的资产价格服从分数布朗运动的几种新型期权定价 总被引:1,自引:1,他引:0
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. 相似文献
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本文讨论了利率服从Vasicek模型时,跳跃扩散模型下欧式期权定价问题.利用特征函数和傅立叶逆反变换,给出了这一模型下欧式看涨期权的定价公式. 相似文献
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考虑跳扩散模型下期权的Esscher变换定价,给出了Esscher变换下带跳的B-S矩生成函数和复合泊松过程下的矩生成函数,推导出跳扩散模型下期权的Esscher变换定价公式. 相似文献
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In this paper we propose a model to price European vulnerable options. We formulate their credit risk in a reduced form model and the dynamics of the spot price in a completely random generalized jump–diffusion model, which nests a number of important models in finance. We obtain a closed-form price for the vulnerable option by (1) determining an equivalent martingale measure, using the Esscher transform and (2) manipulating the pay-off structure of the option four further times, by using the Esscher–Girsanov transform. 相似文献
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Higher order multi-point methods are advantageous to solve scalar nonlinear equations because of their speed of convergence.
The approximate solution is usually obtained in a few steps, thus saving time and computational effort. In this work, we study
the Power Spectrum of the Fourier Transforms of the errors of a well-known family of multi-step Newton method. Firstly, by
two numerical examples we observe that as the order p of the methods increases, the Power Spectrum of Low Frequency modes of successive approximations decreases and the Power
Spectrum of the High Frequency modes increases until they become almost equal when p become large. We prove this point analytically by showing that the Power spectrum of the Fourier Transforms of the errors
of the methods from the error equation is independent of the frequency and the Amplitude of the Power Spectrum tends to zero
as p tends to infinity. From there, we attempt to find the best method of this family. We also compare the family with two other
families of higher order multistep methods, in terms of order, efficiency index and Amplitude of Power Spectrum. Finally,
we conduct more numerical experiments to find the best method of the 3 families.
The work of the first author is partly supported by Tertiary Education Commission and University of Mauritius. 相似文献
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文章研究Esscher变换下标的资产价格服从几何布朗运动的扩展的几种欧式交换期权(包括广义交换期权,复合交换期权,障碍交换期权,红绿灯期权)定价问题.首先,给出了带漂移布朗运动的反射原理和性质;其次,借助Gerber和Shiu (1994)给出了多维独立平稳增量过程和二维带漂移布朗运动的Esscher变换定义及其性质;最后,应用Esscher变换的相关理论给出了标的资产价格服从几何布朗运动的扩展的多种欧式交换期权定价公式.特别,本文所得到的期权定价公式与以往文献中给出的结果是一致的. 相似文献
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Maolin Pan 《Insurance: Mathematics and Economics》2008,42(1):119-126
In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions. 相似文献
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利用分析方法得到了跳扩散模型下美式看涨、看跌期权的价格和最佳实施边界间的对称性公式.美式看涨和看跌期权价格问的对称关系通常是利用概率理论得到,这里给出了这些结果在跳扩散模型下的另一种证明.此外,由本文所得结果和偏微分方程理论,可以得到跳扩散模型下美式看涨期权的最佳实施边界以及永久美式期权的若干性质. 相似文献
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本文在假定标的资产模型依赖时间参数(即无风险利率,标的资产的期望收益率,波动率及红利率),利用已建立的亚式期权定价模型,讨论了上限型期权、抵付型期权、双向型期权等,得到相应的期权定价解析公式. 相似文献
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The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases. 相似文献
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Financial products which depend on hitting times for two underlying assets have become very popular in the last decade. Three common examples are double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions for the joint distribution of the endpoints and the maximum and/or minimum values of two assets are essential in order to obtain quasi-closed form solutions for the price of these derivatives. Earlier authors derived quasi-closed form pricing expressions in the context of constant volatility and correlation. More recently solutions were provided in the presence of a common stochastic volatility factor but with restricted correlations due to the use of a method of images. In this article, we generalize this finding by allowing any value for the correlation. In this context, we derive closed-form expressions for some two-asset barrier options. 相似文献