标题： 方差伽马过程在期权定价中的应用 显示英文标题

标题： The Variance-Gamma Process for Option Pricing

摘要： 本文探讨了在建模股票价格动态中的随机时间次序概念，我们首先介绍了拉普拉斯分布作为高斯方差混合分布的结果，特别是通过绝对矩提出了一种更有效的波动率估计方法。我们将拉普拉斯模型推广，以表征Madan等人提出的强大方差伽马模型，将其作为伽马时间次序的布朗运动，通过埃舍尔变换方法对欧式看涨期权进行定价。我们发现方差伽马模型能够实证地解释对数收益率数据中发现的超额峰度，从而在假设检验中拒绝了布莱克-舒尔斯假设。 显示英文摘要

摘要： This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Laplace model to characterise the powerful variance gamma model of Madan et al. as a Gamma time-subordinated Brownian motion to price European call options via an Esscher transform method. We find that the Variance Gamma model is able to empirically explain excess kurtosis found in log-returns data, rejecting a Black-Scholes assumption in a hypothesis test.