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 present a methodology based on Fourier series analysis to compute time series volatility when the data are observations of a semimartingale. The procedure is not based on the Wiener theorem for the quadratic variation, but on the computation of the Fourier coefficients of the process and...

In general, a comparison Lemma for the solutions of Forward-Backward Stochastic Differential Equations (FBSDE) does not hold. Here we prove one for the backward component at the initial time, relying on certain monotonicity conditions on the coefficients of both components. Such a result is...

We develop the classical asset pricing analysis assuming that the representative agent is characterized by endogenous aspirations. The agent's aspirations at time t are given by a linear combination of the standard of living (habit) at time t (the “forward” part) and of the conditional...

A method is proposed to compute a time-varying correlation matrix between asset prices. The method has a natural geometric interpretation in terms of dynamic principal components analysis. The paper illustrates, via Monte Carlo experiments and data analysis, the potential of the method in...