TIME-CHANGED ORNSTEIN-UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS
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AbstractThis paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Levy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean-reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox-Ingersoll-Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.
All Author(s) ListLi LF, Linetsky V
Journal nameMathematical Finance
Detailed descriptionTo ORKTS: This paper has been accepted and will appear in this journal.
Year2014
Month4
Day1
Volume Number24
Issue Number2
PublisherWILEY-BLACKWELL
Pages289 - 330
ISSN0960-1627
eISSN1467-9965
LanguagesEnglish-United Kingdom
KeywordsBochner subordination; commodity derivatives; commodity futures; commodity options; energy derivatives; jumps; mean reversion; Ornstein-Uhlenbeck; stochastic volatility; time change
Web of Science Subject CategoriesBusiness & Economics; Business, Finance; BUSINESS, FINANCE; Economics; ECONOMICS; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; MATHEMATICS, INTERDISCIPLINARY APPLICATIONS; Social Sciences, Mathematical Methods; SOCIAL SCIENCES, MATHEMATICAL METHODS

Last updated on 2021-02-03 at 01:37