Confidence sets in nonparametric calibration of exponential L\'evy models

TL;DR

This paper develops confidence sets for nonparametric calibration of exponential Lévy models using European option prices, establishing joint asymptotic normality for key estimators.

Contribution

It introduces a spectral calibration method that provides joint confidence sets for multiple parameters in Lévy models, advancing nonparametric calibration techniques.

Findings

Constructed confidence intervals and sets for model parameters.

Proved joint asymptotic normality of estimators.

Applicable to calibration using European option prices.

Abstract

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential L\'evy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift, the jump intensity and the L\'evy density at finitely many points.