Hoang-Long Ngo

An integrated cross-volatility estimation for asynchronous noisy data

Let σ t be the instantaneous cross-volatility of two continuous semimartingales X and Y. In this paper, we introduce some estimators for the class of integrated cross-volatilities of the form where g is a continuous function and processes X and Y are sampled with microstructure noise and in an asynchronous way. In finance, it is widely accepted that the processes X and Y are reasonable models for the log return of price processes of stock and currency and our estimator is relevant in the context of intra-day high-frequency trading.

Weak Approximations for SDE’s Driven by Lévy Processes

In this article we briefly survey recent advances in some simulation methods for Levy driven stochastic differential equations. We give a brief description of each method and extend the one jump scheme method for some subordinated models like the NIG process. Simulations of all the presented methods are performed and compared.