QUANTILE CLOCKS

• 成果类型: Article
• 署名作者: James, Lancelot F.; Zhang, Zhiyuan
• 署名单位: Hong Kong University of Science & Technology; Shanghai University of Finance & Economics
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP752
• 发表日期: 2011
• 页码: 1627-1662
• 关键词: random integral-representations; distributions; functionals; volatility; models

摘要

Quantile clocks are defined as convolutions of subordinators L, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling advantages as business activity times in models for asset prices. We show that the marginal distributions of a quantile clock, at each fixed time, equate with the marginal distribution of a single subordinator. Moreover, we show that there are many quantile clocks where one can specify L, such that their marginal distributions have a desired law in the class of generalized s-self decomposable distributions, and in particular the class of self-decomposable distributions. The development of these results involves elements of distribution theory for specific classes of infinitely divisible random variables and also decompositions of a gamma subordinator, that is of independent interest. As applications, we construct many price models that have continuous trajectories, exhibit volatility clustering and have marginal distributions that are equivalent to those of quite general exponential Levy price models. In particular, we provide explicit details for continuous processes whose marginals equate with the popular VG, CGMY and NIG price models. We also show how to perfectly sample the marginal distributions of more general classes of convoluted subordinators when L is in a sub-class of generalized gamma convolutions, which is relevant for pricing of European style options.