A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence

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• 作者：Enrico Bibbona ; Laura Sacerdote…
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：18
• 期：3
• 页码：765-783
• 全文大小：483 KB
• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713
• 卷排序：18

文摘

This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This approach provides a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models.KeywordsCopulaeCopulasSpace-time transformationsDiffusionsSerial dependenceStochastic differential equations