We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total...

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy...

We study the nonparametric calibration of exponential, self-decomposable Lévy models whose jump density can be characterized by the k-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, the activity measure a := k(0+) + k(0-) and analog parameters for...

We introduce a novel semi-parametric estimator of the price of American options in a discrete time, Markovian framework. The estimator is based on a parametric specification of the stochasticdiscount factor and is non-parametric w.r.t. the historical dynamics of the state variables. The...

A Lévy process is observed at time points of distance delta until time T. We construct an estimator of the Lévy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and delta. Thereby, we encompass the usual low- and high-frequency assumptions...

In this paper we propose a novel method to construct confidence intervals in a class of linear inverse problems. First, point estimators are obtained via a spectral cut-off method depending on a regularisation parameter α, that determines the bias of the estimator. Next, the proposed confidence...

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable. Under these conditions the nonseparable model is...

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the...

Sellers of variance swaps earn time-varying risk premia for their exposure to realized variance, the level of variance swap rates, and the slope of the variance swap curve. To measure risk premia, we estimate a dynamic term structure model that decomposes variance swap rates into expected...