文章基本信息

标题：Continuous Mixed-Laplace Jump Diffusion Models for Stocks and Commodities
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作者：Azmier Adib ; Mardiastuti H.Wahid ; Pratiwi Sudarmono 等
期刊名称：Quantitative Finance and Economics
电子版ISSN：2573-0134
出版年度：2017
卷号：1
期号：2
页码：145-173
DOI：10.3934/QFE.2017.2.145
语种：English
出版社：AIMS Press
摘要：This paper proposes two jump diffusion models with and without mean reversion, for stocks or commodities, capable to fit highly leptokurtic processes. The jump component is a continuous mixture of independent point processes with Laplace jumps. As in financial markets, jumps are caused by the arrival of information and sparse information has usually more importance than regular information, the frequencies of shocks are assumed inversely proportional to their average size. In this framework, we find analytical expressions for the density of jumps, for characteristic functions and moments of log-returns. Simple series developments of characteristic functions are also proposed. Options prices or densities are retrieved by discrete Fourier transforms. An empirical study demonstrates the capacity of our models to fit time series with a high kurtosis. The Continuous Mixed-Laplace Jump Diffusion (CMLJD) is fitted to four major stocks indices (MSWorld, FTSE, S & P and CAC 40), over a period of 10 years. The mean reverting CMLJD is fitted to four time series of commodity prices (Copper, Soy Beans, Crude Oil WTI and Wheat), observed on four years. Finally, examples of implied volatility surfaces for European Call options are presented. The sensitivity of this surface to each parameters is analyzed.
关键词：jump diffusion model;options;mixed-exponential distributions;double exponential jump diffusion