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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert


SCImago Journal Rank (SJR) 2015: 0.105

Mathematical Citation (MCQ) Quotient 2014: 0.14

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2196-7040
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Method of moment estimation in time-changed Lévy models

Jan Kallsen1 / Johannes Muhle-Karbe*

1 Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar, Kiel, Deutschland

* Correspondence address: ETH Zürich, Department Mathematik, Rämistr. 101, 8092 Zürich, Schweiz,

Citation Information: Statistics & Decisions International mathematical journal for stochastic methods and models. Volume 28, Issue 2, Pages 169–194, ISSN (Print) 0721-2631, DOI: 10.1524/stnd.2011.1076, May 2011

Publication History

Published Online:
2011-05-31

Abstract

This paper introduces a method of moment estimator for the time-changed Lévy processes proposed by Carr, Geman, Madan and Yor (2003). By establishing that the returns sequence is strongly mixing with exponentially decreasing rate, we prove consistency and asymptotic normality of the resulting estimators. In addition, we fit parametrized versions of the model to real data and examine the quality of our estimators by performing a simulation study. Finally, we also show how to estimate the current level of volatility.

Keywords: time-changed Lévy models; moment estimator; mixing property; volatility estimation

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