跳跃-扩散模型基于拉普拉斯变换的参数估计
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摘要
文章基于拉普拉斯变换的估计原理是令模型理论拉普拉斯变换与数据经验拉普拉斯变换相匹配,是当似然函数不存在或者是其形式复杂而对应的拉普拉斯变换相对简单时,最大似然估计(MLE)的一种有效替代。当变换变量与估计参数相关时,使用自适应估计量和经验最小方差估计量两种解决方式,以获得有效的拉普拉斯变换估计量,并利用Matlab软件编程将其应用于金融随机模型跳跃-扩散模型中,为解决实际金融产品及其衍生产品的定价等问题的研究提供恰当的参数估计方法。
This paper is based on the fact that the estimation principle of Laplace transform is to match the Laplace transform of model theory with the data experience Laplace transform,and is also an effective substitute of maximum likelihood estimation(MLE) when the likelihood function does not exist or is complex and the corresponding Laplace transform is relatively simple.When the transformation variable is related to the estimated parameters,two solutions,adaptive estimator and empirical minimum variance estimator,are used to obtain effective Laplace transform estimator,and Matlab software programming is applied to the financial stochastic model of jump-diffusion model,which provides an appropriate parameter estimation method for the study of pricing of real financial products and their derivatives.
This paper is based on the fact that the estimation principle of Laplace transform is to match the Laplace transform of model theory with the data experience Laplace transform,and is also an effective substitute of maximum likelihood estimation(MLE) when the likelihood function does not exist or is complex and the corresponding Laplace transform is relatively simple.When the transformation variable is related to the estimated parameters,two solutions,adaptive estimator and empirical minimum variance estimator,are used to obtain effective Laplace transform estimator,and Matlab software programming is applied to the financial stochastic model of jump-diffusion model,which provides an appropriate parameter estimation method for the study of pricing of real financial products and their derivatives.
引文
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[6]Imbens G W.Generalized Method of Moments and Empirical Likelihood[J].Journal of Business and Economic Statistics,2002,20(4).
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[8]Robert C P,Casella G.Monte Carlo Statistical Method[M].New York:Springer,1999.
[9]Yu J.Empirical Characteristic Function Estimation and Its Applications[J].Econometric Reviews,2004,23(2)./
[2]Ball F G,Milne R K.On Choosing Values of the Transform Variables in Empirical Transform Based Inference[J].Perth,Western Australia,1996,(25).
[3]Yao Q,Morgan B J T.Empirical Transform Estimation for Indexed Stochastic Models[J].Journal of the Royal Statistical Society:Series B(Statistical Methodology),1999,61(1).
[4]Besbeas P,Morgan B J T.Improved Estimation of the Stable Laws[J].Statistics and Computing Archive,2008,18(2).
[5]Carrasco M,Florens J P.Efficient GMM Estimation Using the Empirical Characteristic Function[J].Idei Working Papers,2002.
[6]Imbens G W.Generalized Method of Moments and Empirical Likelihood[J].Journal of Business and Economic Statistics,2002,20(4).
[7]Kou S.A Jump-diffusion Model for Option Pricing[J].Management Science,2002,(48).
[8]Robert C P,Casella G.Monte Carlo Statistical Method[M].New York:Springer,1999.
[9]Yu J.Empirical Characteristic Function Estimation and Its Applications[J].Econometric Reviews,2004,23(2)./