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1.
The relative entropy in CGMY processes and its applications to finance   总被引:1,自引:0,他引:1  
The CGMY market model generates infinite equivalent martingale measures (EMM). In order to price options, we need an adequate method to choose one EMM. This paper presents the relative entropy for CGMY processes, and apply it to choosing an EMM called the model preserving minimal entropy martingale measure.   相似文献
2.
GARCH option pricing: A semiparametric approach   总被引:1,自引:0,他引:1  
Option pricing based on GARCH models is typically obtained under the assumption that the random innovations are standard normal (normal GARCH models). However, these models fail to capture the skewness and the leptokurtosis in financial data. We propose a new method to compute option prices using a nonparametric density estimator for the distribution of the driving noise. We investigate the pricing performances of this approach using two different risk neutral measures: the Esscher transform pioneered by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1994a. Option pricing by Esscher transforms (with discussions). Trans. Soc. Actuar. 46, 99–91], and the extended Girsanov principle introduced by Elliot and Madan [Elliot, R.J., Madan, D.G., 1998. A discrete time equivalent martingale 9 measure. Math. Finance 8, 127–152]. Both measures are justified by economic arguments and are consistent with Duan’s [Duan, J.-C., 1995. The GARCH option pricing model. Math. Finance 5, 13–32] local risk neutral valuation relationship (LRNVR) for normal GARCH models. The main advantage of the two measures is that one can price derivatives using skewed or heavier tailed innovations distributions to model the returns. An empirical study regarding the European Call option valuation on S&P500 Index shows: (i) under both risk neutral measures our semiparametric algorithm performs better than the existing normal GARCH models if we allow for a leverage effect and (ii) the pricing errors when using the Esscher transform are quite small even though our estimation procedure is based only on historical return data.  相似文献
3.
本文讨论了股票价格对数过程由复合泊松过程、Meixner过程驱动下的欧式看涨期权的定价问题.利用Esscher变换和风险中性Esscher测度得到了两类过程驱动下的期权定价公式,为实践者提供了理论上的参考价格.  相似文献
4.
权益指数年金(Equity Indexed Annuities)是欧美市场近十年发展起来的一类新型年金产品,有最小收益保证,在最小保证基础上与预先设定好的某类股指收益相关联.本文在考虑死亡风险情况下,对简单点对点和年度重设两种指数计算方法下权益指数年金的定价问题作了研究,给出了定价公式并对参与率作了敏感性分析.  相似文献
5.
万建平  冯雅琴  冯文 《经济数学》2007,24(2):139-146
近年来,公司为了吸引和激励股票的执行者而引入了一系列的非传统期权.本文将讨论其中的一种:再装期权,运用Esscher变换给出了再装期权(只装一次)的闭式解,并提供了数值计算的例子,为实践者提供了理论上的参考价格.  相似文献
6.
J. M. P. Albin 《Extremes》2004,7(3):199-220
Let be a sequence of independent identically distributed positive random variables with O-regularly varying distribution F at 0. Given a sequence of positive numbers, we show that belongs to the Type I domain of attraction of extremes for minima, by means of relating the asymptotic behaviour of P{S < } as 0, to that of E{e-S/}. Our contribution is that we dispense with the unnatural moment condition from the literature, that F has finite variance. This in turn permits a novel application to lower tails of -stable distributions on Hilbert space.AMS 2000 Subject Classification. Primary—60G50, 60G70, Secondary—60B12, 60E07, 60F05, 60G52Research supported by NFR Grant M 650-19981841/2000, and by M.R. Leadbetter  相似文献
7.
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.  相似文献
8.
Let be Euler's Gamma function. We prove that, for all 0, > 0, > 0, > 0, the function (( + iz)/() i z) , z R 1, is a self-decomposable characteristic function from the Thorin class and derive its explicit canonical form. Similarly to [1], we also describe several classes of Lévy-type stochastic processes related to .  相似文献
9.
The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.  相似文献
10.
A compound Poisson process is of the form where Z, Z 1, Z 2, are arbitrary i.i.d. random variables and N is an independent Poisson random variable with parameter . This paper identifies the degree of precision that can be achieved when using exponential bounds together with a single truncation to approximate . The truncation level introduced depends only on and Z and not on the overall exceedance level a.  相似文献
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