深圳大学学报（理工版）
深圳大學學報（理工版）
심수대학학보（리공판）
JOURNAL OF SHENZHEN UNIVERSITY (SCIENCE & ENGINEERING)
2014年
3期
325-330
,共6页
应用统计数学%Lévy过程%期权定价%极大似然参数估计%特征函数%快速傅里叶变换
應用統計數學%Lévy過程%期權定價%極大似然參數估計%特徵函數%快速傅裏葉變換
응용통계수학%Lévy과정%기권정개%겁대사연삼수고계%특정함수%쾌속부리협변환
application of statistical mathematics%Lévy process%option pricing%maximum likelihood parameter es-timation%characteristic function%fast Fourier transform
Lévy过程可准确描述某些复杂的分布特征,如：尖峰、厚尾及有偏等,也可将标的资产运动过程中所展现的非连续性体现出来,因此在金融过程中得到了广泛而有效的运用。本研究基于期权的定价公式,运用极大似然法以及快速傅里叶变换对方差伽马( Variance-Gamma, VG)模型、 Carr-Geman-Madan-Yor ( CGMY)模型及VGSA模型( VG和Cox-Ingersoll-Ross模型的复合指数模型)等几种典型Lévy过程的参数进行有效估计,并且通过香港恒生指数期权数据对该方法进行验证。
Lévy過程可準確描述某些複雜的分佈特徵,如：尖峰、厚尾及有偏等,也可將標的資產運動過程中所展現的非連續性體現齣來,因此在金融過程中得到瞭廣汎而有效的運用。本研究基于期權的定價公式,運用極大似然法以及快速傅裏葉變換對方差伽馬( Variance-Gamma, VG)模型、 Carr-Geman-Madan-Yor ( CGMY)模型及VGSA模型( VG和Cox-Ingersoll-Ross模型的複閤指數模型)等幾種典型Lévy過程的參數進行有效估計,併且通過香港恆生指數期權數據對該方法進行驗證。
Lévy과정가준학묘술모사복잡적분포특정,여：첨봉、후미급유편등,야가장표적자산운동과정중소전현적비련속성체현출래,인차재금융과정중득도료엄범이유효적운용。본연구기우기권적정개공식,운용겁대사연법이급쾌속부리협변환대방차가마( Variance-Gamma, VG)모형、 Carr-Geman-Madan-Yor ( CGMY)모형급VGSA모형( VG화Cox-Ingersoll-Ross모형적복합지수모형)등궤충전형Lévy과정적삼수진행유효고계,병차통과향항항생지수기권수거대해방법진행험증。
The Lévy process can accurately describe the complex features of distribution, such as spikes, fat tails, and the discontinuity of the underlying asset reflected in the movement. Thus, the application of the Lévy processes in financial engineering becomes extensive and effective. However, estimation of the Lévy process parameters is diffi-cult. Based on the option pricing formula, we used the maximum likelihood method and the fast Fourier transforms to make valid estimation on several typical Lévy process parameters, including the Variance-Gamma ( VG ) model, Carr-Geman-Madan-Yor ( CGMY ) model and VGSA ( the exponential form for combining VG with Cox-Ingersoll-Ross) model. The method is tested by the Hong Kong Hang Sheng Index Options data, which is important to pro-mote the achievements of previous results which focus on the Lévy parameter estimation.
