TIME-CHANGED ORNSTEIN-UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS
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摘要This 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.
著者Li LF, Linetsky V
期刊名稱Mathematical Finance
詳細描述To ORKTS: This paper has been accepted and will appear in this journal.
出版年份2014
月份4
日期1
卷號24
期次2
出版社WILEY-BLACKWELL
頁次289 - 330
國際標準期刊號0960-1627
電子國際標準期刊號1467-9965
語言英式英語
關鍵詞Bochner subordination; commodity derivatives; commodity futures; commodity options; energy derivatives; jumps; mean reversion; Ornstein-Uhlenbeck; stochastic volatility; time change
Web of Science 學科類別Business & 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

上次更新時間 2021-11-04 於 00:14