The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives, and mainly for fitting stochastic model with the fundamental probabilistic relationships of infinite divisibility. The probability density functions are computed, and the distributional proprieties are reviewed for Variance-Gamma (VG) model. The VG model has been increasingly used as an alternative to the Classical Lognormal Model (CLM) in modelling asset prices. The VG model was estimated by the FRFT. The data comes from the SPY ETF historical data. The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits the cumulative distribution of the sample data better than the CLM. The best VG model comes from the FRFT estimation.
翻译:本文审查了基于小数方形Fourier变形(FFFT)的技术,作为获取概率密度函数及其衍生物的工具,主要用于将随机模型与无限可视性的基本概率关系相匹配。概率密度函数是计算出来的,分配特性功能是为差异-伽马(VG)模型进行的审查。在模拟资产价格时,VG模型越来越多地被用作古典逻辑正常模型的替代物。VG模型由FFFT估算。数据来自SPY ETF的历史数据。Kolmogorov-Smirnov(KS)的优点显示,VG模型比CLM更好地符合样本数据的累积分布。最佳VG模型来自FFT的估计。