This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions...

Supported by several recent investigations, the empirical pricing kernel (EPK) puzzle might be considered a stylized fact. Based on an economic model with state dependent preferences for the financial investors, we want to emphasize a microeconomic view that succeeds in explaining the puzzle. We...

This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a...

Pricing kernels play a major role in quantifying risk aversion and investors' preferences. Several empirical studies reported that pricing kernels exhibit a common pattern across different markets. Mostly visual inspection and occasionally numerically summarise are used to make comparison. With...

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,...

The new aspect is that neither assumptions on compactness of the inner approximating lattices nor nonsequential continuity properties for the measures will be imposed. As a providing step also a generalization of the classical Portmanteau lemma will be established. The obtained characterizations...

A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk...

Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most...