Option calibration of exponential L\'evy models: Confidence intervals and empirical results

TL;DR

This paper develops a nonparametric calibration method for exponential Lévy models using option prices, providing confidence intervals for key parameters and demonstrating good empirical performance on market data.

Contribution

It introduces efficient spectral estimation procedures for both finite and infinite jump activity Lévy models, including confidence interval construction and empirical validation.

Findings

Confidence intervals perform well in size and coverage.

Both finite and infinite jump activity models achieve good calibration.

Finite activity model shows stability over multiple trading days.

Abstract

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.