We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous. The central limit theorem is shown to have a feasible version. In the process, we show that the...

Equity basket correlation is an important risk factor. It characterizes the strength of linear dependence between assets and thus measures the degree of portfolio diversification. It can be estimated both under the physical measure from return series, and under the risk neutral measure from...

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time...

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A...

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface...

We model the dynamics of ask and bid curves in a limit order book market using a dynamic semiparametric factor model. The shape of the curves is captured by a factor structure which is estimated nonparametrically. Corresponding factor loadings are assumed to follow multivariate dynamics and are...

Over recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical...

We propose a general class of Markov-switching-ARFIMA processes in order to combine strands of long memory and Markov-switching literature. Although the coverage of this class of models is broad, we show that these models can be easily estimated with the DLV algorithm proposed. This algorithm...

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

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...