Sigurd Nellemann Thorsen defends his PhD thesis at the Department of Economics

Candidate:

Sigurd Nellemann Thorsen, Department of Economics, University of Copenhagen

Title:

Essays in Financial Econometrics

Supervisors:

  • Anders Rahbek, Professor, Department of Economics, University of Copenhagen
  • Rasmus Søndergaard Pedersen, Associate Professor, Department of Economics, University of Copenhagen

Assessment Committee:

  • Henrik Hansen, Professor, Department of Economics, University of Copenhagen
  • Dennis Kristensen, Professor, Department of Economics, University College London
  • Leopoldo Catania, Associate Professor, Department of Economics and Business Economics, Aarhus University

Summary:

This PhD dissertation consists of three separate and self-contained chapters within financial econometrics. All the chapters include econometric theory, a simulation experiment of the asymptotic results, and an empirical application of the paper’s methodology.

The first chapter of my dissertation is joint work with Heino B. Nielsen, Rasmus S. Pedersen, and Anders Rahbek. The chapter examines the GARCH-X model and focuses on the hypothesis of testing the inclusion of explanatory variables in the conditional variance equation. Due to the boundary constraints on nuisance parameters, the likelihood-ratio (LR) test statistic has a non-standard limiting distribution, complicating inference. To address this issue, we introduce the "Fixed Shrinkage" (FS) bootstrap method, which is carefully tailored to this testing problem in the GARCH-X model and correctly replicates the limiting distribution of the LR statistic.  In an extensive Monte Carlo simulation study, we investigate our proposed FS bootstrap method's empirical size and power properties and find that it shows great finite sample properties. We illustrate the usefulness of our proposed bootstrap in an application on volatility modeling of stock market indices. 

In the second chapter, we consider backtesting Value-at-Risk (VaR), which is subject to estimation risk in the class of volatility models on the form rt = δtηt. The paper focuses on the widely used unconditional coverage (UC) and conditional coverage (CC) tests from Christoffersen (1998), and we illustrate when VaR estimates are subject to estimation risk, the standard limiting X2 (1) and X2 (2) distributions typically used for backtesting are generally no longer valid.  To account for estimation risk in VaR estimates, we propose an easily implemented correction for the UC test and a simple simulation-based method to obtain critical values for the CC test statistic. Through a Monte Carlo simulation study, we showcase our theory in finite samples and find that our corrected tests display attractive size properties. In an empirical application, we highlight the GARCH-X model augmented with realized volatility (RV) for risk management.

In the third chapter, we investigate the temporal dependence in option observation errors, which is previously unexplored in the literature. The asymptotic setting is infill type, with the time between options shrinking to zero and the log-strike values of neighboring options in the cross-section shrinking to zero. To test for temporal dependence in option observation errors, we propose a Portmanteau test statistic, which, under the null hypothesis of no temporal dependence in the option observation errors, has a standard limiting chi-squared distribution. We obtain good finite sample properties for our proposed inference methods in an empirically relevant simulation setting. By applying our methodology to high-frequency S&P 500 index options, we find considerable evidence of temporal dependence in option observation errors subject to a large degree of heterogeneity across maturities of the options and their range of strike values.

 

An electronic copy of the dissertation can be requested here: lema@econ.ku.dk