Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the  implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as for self-decomposable L\'evy models and improve these methods. Confidence intervals are constructed for the estimators in the finite activity case. They allow inference on the behavior of the parameters when the option prices are observed in a sequence of trading days . We compare the performance of the procedures for finite and infinite jump activity based on real option data .
Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as for self-decomposable L\'evy 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 .
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efficient
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and improve these methods. Confidence
. Based on finite sample variances, confidence
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estimators in the finite activity case. They allow inference on the behavior of the parameters when the option prices are observed in a sequence of trading days
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
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real option data
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