High-dimensional regression problems which reveal dynamic behavior are typicallyanalyzed by time propagation of a few number of factors. The inference on thewhole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different...

Implied volatility is one of the key issues in modern quantitative finance, since plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount of...

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

Nonparametric estimators of autocovariance functions for non-stationary time series are developed. The estimators are based on straightforward nonparametric mean function estimation ideas and allow use of any linear smoother (e.g. smoothing spline, local polynomial). We study the properties of...

In this paper, we develop a new asymptotic theory of the long run variance estimator obtained by fitting a vector autoregressive model to the transformed moment processes in a GMM framework. In contrast to the conventional asymptotics where the VAR lag order p goes to infinity but at a slower...

In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at...

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

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and...

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an...