Option calibration of exponential Lévy models: Confidence intervals and empirical results

Jakob Söhl, Mathias Trabs

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models. Based on finite sample variances, confidence intervals are constructed for the volatility, for the drift and, pointwise, for the jump density. As demonstrated by simulations, these intervals perform well in terms of size and coverage probabilities. We compare the performance of the procedures for finite and infinite jump activity based on options on the German DAX index and find that both methods achieve good calibration results. The stability of the finite activity model is studied when the option prices are observed in a sequence of trading days.

Original languageEnglish
Pages (from-to)91-119
Number of pages29
JournalThe Journal of Computational Finance
Volume18
Issue number2
DOIs
Publication statusPublished - 1 Dec 2014
Externally publishedYes

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