In order to study the geometry of interest rates market dynamics, Malliavin, Mancino and Recchioni [A non-parametric calibration of the HJM geometry: an application of It\^o calculus to financial statistics, {\it Japanese Journal of Mathematics}, 2, pp.55--77, 2007] introduced a scheme, which is...

We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the l-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume...

We study the forecasting performance of the Fourier volatility estimator in the presence of microstructure noise. Analytical comparison and simulation studies indicate that the Fourier estimator significantly outperforms realized volatility type estimators in particular for high frequency data...

The economic benefit of applying the Fourier covariance estimation methodology over other estimators in the presence of market microstructure noise is studied from the perspective of an asset-allocation decision problem. We find that using Fourier methodology yields statistically significant gains

We analyze the effects of market microstructure noise on the Fourier estimator of multivariate volatilities. We prove that the estimator is consistent in the case of asynchronous data and robust in the presence of microstructure noise. This result is obtained through an analytical computation of...