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...

We present two methods based on functional principal component analysis (FPCA) for the estimation of smooth derivatives of a sample of random functions, which are observed in a more than one-dimensional domain.We apply eigenvalue decomposition to a) the dual covariance matrix of the derivatives,...

This study provides an in-depth analysis of how to estimate risk-neutral moments robustly. A simulation and an empirical study show that estimating risk- neutral moments presents a trade-off between (1) the bias of estimates caused by a limited strike price domain and (2) the variance of...

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for...

Option prices seem to behave in ways inconsistent with the Black-Scholes model. Implied volatility varies with the strike price in a parabolic shape that is often called the volatility 'smile.' My objective in this paper is to identify implied probability distributions that might explain this...

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied...

In this paper we will be estimating risk-neutral densities (RND) for the largest euro area stock market (the index of which is the German DAX), reporting their statistical properties, and evaluating their forecasting performance. We have applied an innovative test procedure to a new, rich, and...

We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest many standard models as special cases. The loss...

We generalize the Kou (2002) double exponential jump-diffusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape...