B1658
Title: Spectral calibration of time-inhomogeneous exponential Levy models
Authors: Loek Koorevaar - IMC Trading (Netherlands)
Jakob Soehl - Delft University of Technology (Netherlands) [presenting]
Stan Tendijck - Shell (Netherlands)
Abstract: Empirical evidence shows that calibrating exponential Levy models by options with different maturities leads to conflicting information. In other words, the stationarity implicitly assumed in the exponential Levy model is not satisfied. An identifiable time-inhomogeneous Levy model is proposed that does not assume stationarity and that can integrate option prices from different maturities and different strike prices without leading to conflicting information. In the time-inhomogeneous Levy model, the convergence rates are derived, and confidence intervals are shown for the estimators of the volatility, the drift, the intensity and the Levy density. Previously, confidence intervals have been constructed for time-homogeneous Levy models in an idealized Gaussian white noise model. In the idealized Gaussian white noise model, it is assumed that the observations are Gaussian and given continuously across the strike prices. This simplifies the analysis significantly. The confidence intervals are constructed in a discrete observation setting for time-inhomogeneous Levy models, and the only assumption on the errors is that they are sub-Gaussian. In particular, all bounded errors with arbitrary distributions are covered. Additional results on the convergence rates extend existing results from time-homogeneous to time-inhomogeneous Levy models.
