This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in...

A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure...

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...

The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is...

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...

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant...

As a consequence of recent technological advances and the proliferation of high-frequency trading and other forms of algorithmic trading, the cost of trading in financial markets has irrevocably changed. One important change relates to how trading affects prices; this is known as price impact....

We present a new nonparametric method for fitting the term structure of interest rates from bond prices. Our method is a variant of the smoothing spline approach, but within our framework we are able to determine the smoothing coefficient automatically from the data using generalized...

We propose a nonparametric method to study which characteristics provide incremental information for the cross section of expected returns. We use the adaptive group LASSO to select characteristics and to estimate how they affect expected returns nonparametrically. Our method can handle a large...