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1 Dipartimento di Matematica e Informatica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy 2 CERI-Centro di Ricerca “Previsione, Prevenzione e Controllo dei Rischi Geologici”, Università di Roma “La Sapienza”, Palazzo Doria Pamphilj, Piazza Umberto Pilozzi 9, Valmontone 00038 Roma, Italy 3 Dipartimento di Scienze Sociali “D.… (More)

A multiscale SABR model that describes the dynamics of forward prices/rates is presented. New closed form formulae for the transition probability density functions of the normal and lognormal SABR and multiscale SABR models and for the prices of the corresponding European call and put options are deduced. The technique used to obtain these formulae is… (More)

- Vincent D. Blondel, Alexander Megretski, +17 authors Bart De Moor
- 1999

Some of the problems appearing in this booklet will appear in a more extensive forthcoming book on open problems in systems theory. For more information about this future book, please consult the website We wish the reader much enjoyment and stimulation in reading the problems in this booklet.

The SABR stochastic volatility model with β-volatility β є (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition… (More)

Variance and volatility derivatives are becoming increasingly important in the financial markets. To fix the ideas let γn, n = 0, 1, 2, . . . , N be a time series of consecutive prices of an asset, such as, for example, the daily closing value of a market index, observed at time tn, n = 0 (today),1, 2, . . . , N (maturity). For n = 1, 2, . . . , N holding a… (More)

- Lorella Fatone, Pierluigi Maponi, Francesco Zirilli
- Systems, Control, Modeling and Optimization
- 2006

We study the problem of urban areas detection from satellite images. In particular, we consider two types of satellite images: SAR (Synthetic Aperture Radar) images and optical images. We describe a simple algorithm for the detection of urban areas. We show that the performance of the detection algorithm can be improved using a fusion procedure of the SAR… (More)

- Danielle Blondel, Alexander Megretski, +15 authors Bart De Moor
- 2007

A highly parallelizable numerical method to solve three-dimensional time-dependent acoustic obstacle scattering problems involving passive or smart, furtive, realistic obstacles is presented. ‘‘Realistic’’ obstacles have complex geometries, ‘‘passive’’ obstacles do not react by taking an action to pursue a goal when hit by an incoming wave, and ‘‘smart… (More)

- Lorella Fatone, Marco Giacinti, Francesca V Mariani, Maria Cristina Recchioni, Francesco Zirilli
- The Journal of Supercomputing
- 2012

This paper shows two examples of how the analysis of option pricing problems can lead to computational methods efficiently implemented in parallel. These computational methods outperform “general purpose” methods (i.e., for example, Monte Carlo, finite differences methods). The GPU implementation of two numerical algorithms to price two specific derivatives… (More)

- Lorella Fatone, Daniele Funaro, Valentina Scannavini
- 2007

The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of… (More)

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