TY - JOUR
T1 - Option calibration of exponential Lévy models
T2 - Confidence intervals and empirical results
AU - Söhl, Jakob
AU - Trabs, Mathias
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84893682125&partnerID=8YFLogxK
U2 - 10.21314/JCF.2014.275
DO - 10.21314/JCF.2014.275
M3 - Article
AN - SCOPUS:84893682125
SN - 1460-1559
VL - 18
SP - 91
EP - 119
JO - The Journal of Computational Finance
JF - The Journal of Computational Finance
IS - 2
ER -