Simulation and Estimation of General Tempered Lévy Distributions

• Applicant: Dr. Till Massing
• Subject Area: Statistics and Econometrics ; Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 455257011

• Final Report Year: 2024

Final Report Abstract

In this project, simulation and estimation methods for tempered stable distributions were comprehensively investigated. These specific distributions are often used to model complex price processes of financial market instruments and to value options, as they can realistically capture both heavy tails and jumps in the data. However, traditional estimation methods for tempered stable distributions often reach their limits, being either numerically imprecise or statistically inefficient. To address these gaps, several innovative estimation methods were developed and thoroughly tested within the project. The focus was on improving estimation quality, i.e., the accuracy and efficiency of the methods. In addition to theoretical analysis, practical implementations were developed and published as software routines. These tools significantly simplify the application of the new methods and promote their use in empirical research. Another key aspect of the project was the development of efficient simulation methods. Particular emphasis was placed on the simulation of time-dependent tempered stable random variables, as these play a central role in modeling dynamic financial market processes. The theoretical insights and developed methods were subsequently successfully applied to the modeling of financial market time series, including specific applications such as electricity price time series, which pose a particular challenge due to their high volatility and nonlinear properties.

Publications

• Approximation and error analysis of forward–backward SDEs driven by general Lévy processes using shot noise series representations. ESAIM: Probability and Statistics, 27, 694-722.
  Massing, Till
  
• „TempStable: A Collection of Methods to Estimate Parameters of Different Tempered Stable Distributions“. R Package.
  Massing, T. & Jüssen, C.
  
• Parametric Estimation of Tempered Stable Laws. Latin American Journal of Probability and Mathematical Statistics, 21(2), 1567.
  Massing, Till