Il giorno giovedì 17 luglio alle ore 14.30 presso la Sala del Consiglio della Scuola di Economia e Statistica, al IV piano dell'edificio U7 in via Bicocca degli Arcimboldi 8, si terrà il mini-workshop "Young Researchers" con il seguente programma: 14.30 - 15.00 Annamaria Gambaro, Dottorato in Statistica e Matematica per la Finanza, Curriculum Matematica per la Finanza, Università di Milano-Bicocca Approximated pricing of swaptions in general interest rate models We propose a new lower bound on the prices of European-style swaptions for a wide class of interest rate models. This method is applicable whenever the joint characteristic function of the state variables is known in closed form or could be easily obtained with numerical PDE solution method. Our algorithm involves the computation of one dimensional Fourier transform indipendently from the swap length. Moreover the bound could be used as a control variable to reduce confidence interval of the Monte Carlo technique. We test our new lower bound on different affine models and on 2-factor quadratic gaussian model and the method is found to be fast and accurate (joint work with Ruggero Caldana and Gianluca Fusai). 15.00 - 15.30 Jacopo Corbetta, Dottorato in Matematica e Applicazioni, Università di Milano-Bicocca Smile asymptotics in a multiscaling stochastic volatility model We consider a stochastic volatility model which captures some relevant stylized facts of financial series, including the so-called multiscaling of moments. We obtain sharp large deviations estimates for the price, based on a large deviations principle for suitable functionals of a point process, which is of independent interest. This yields explicit asymptotic formulas for the price of European options, and for the related implied volatility, both in the small maturity and large strike regimes. In particular, we show that implied volatility for out-of-the-money options explodes as the maturity vanishes, with an explicit limiting shape (joint work with Francesco Caravenna). 15.30 - 16.00 Alberto Santangelo, Dottorato in Statistica e Matematica per la Finanza, Curriculum Matematica per la Finanza, Università di Milano-Bicocca Measuring Portfolio Diversification Based on Optimized Uncorrelated Factors We measure diversification in terms of the "Effective Number of Minimum-Torsion Bets", namely a set of uncorrelated factors, optimized to closely track the factors used to allocate the portfolio. In this way we introduce a novel notion of "absolute risk contributions", which generalizes the "marginal contributions to risk" in traditional risk parity. We discuss the advantages of the Minimum-Torsion Bets over the traditional approach to diversification based on marginal contributions to risk. We present a case study in the S&P 500. Fully documented code is available for download (joint work with Romain Deguest and Attilio Meucci). Tutti gli interessati sono invitati a partecipare. Prof. Fabio Bellini Department of Statistics and Quantitative Methods University of Milano-Bicocca Via Bicocca degli Arcimboldi 8, 20126 Milano 0039-2-64483119 http://www.economia.unimib.it/bellini