TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS

By Lingfei Li, Vadim Linetsky. 2012

73 citations recorded by the source corpus.

This paper studies subordinate Ornstein–Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e45669f85da34a797ca4d1fb5d303964ad575e63

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Rafael Mendoza-Arriaga
2. Vadim Linetsky

In Finance

1. Rafael Mendoza-Arriaga
2. Vadim Linetsky
3. Lingfei Li
4. Jian-wei Gao
5. Wim Schoutens
6. Marceau Decamps
7. Marc J. Goovaerts

Citations in the corpus

• Error analysis of finite difference and Markov chain approximations for option pricing (2018, unknown): “See, e.g., Mendoza-Arriaga et al. (2010) for unified credit-equity modeling and Li and Linetsky (2014) and Li et al. (2016) for applications in commodity markets.”
• Time-changed CIR default intensities with two-sided mean-reverting jumps (2014, methodology): “where an extensive bibliography is given. Recent applications of subordinate diffusion models in finance can be found in Boyarchenko and Levendorski˘ı (2007), Mendoza-Arriaga, Carr and Linetsky (2010), Li and Linetsky (2013a, 2013b), Mendoza-Arriaga and Linetsky (2013), Lim, Li and Linetsky (2012). He”
• Electricity price modeling with stochastic time change (2017, unknown): “One exception is Li and Linetsky [22], who combine a mean reverting model for commodity prices with a time change and derive futures and option prices in terms of Hermite expansions.”