---------- Forwarded message ---------- Date: Fri, 27 Nov 2015 16:21:41 +0100 From: Pietro Rossi pietro.rossi@prometeia.com To: Tiziano Vargiolu vargiolu@math.unipd.it Subject: Annuncio di seminario

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Giovedi 3 Dicembre ore 14:30

Anna Maria Gambaro Dottoranda presso il dipartimento di statistica e metodi quantitativi (DISMEQ) dell'universit? di Milano Bicocca

HJM multiple-curve model with time-changed L?vy processes

Abstract:We propose a multiple-curve model, set in Heath-Jarrow-Morton framework, with time-changed L ?evy as driving processes. This class of process was introduced in finance by Carr and Wu (2004) for pricing of equity derivatives. However, recently, empirical studies, as Leippold and Str?mberg (2014), suggest the application of time-changed L ?evy process to interest rate financial products. In particular, L ?evy processes generate very flexible return innovation distribution and take into account potential discontinuities in Libor dynamics. On the other hand, the time change and the dependence between the L ?evy process and the random time introduce ?stochastic volatility? and ?stochastic skew? in the model, in order to reproduce the term structure of the volatility smile of caps and swaptions. This paper is inspired by the work of Eberlein and Raible (1999) on L ?evy models, generalized in Crepey et al. (2014) to a multiple curve setting. To the best of our knowledge, no previous works present a theoretically consistent no-arbitrage framework for pricing interest rate derivatives with time-changed L ?evy process. Moreover we apply these flexible processes to a multiple-curve post crisis set-up. First of all, we build a term structures for zero coupon bonds and Libor forward rate and we derive sufficient conditions to ensure the absence of arbitrage. Moreover the pricing of interest rate derivatives, as caps and swaptions, is developed using the Fourier transform method. Finally different choices for the construction of the driving process are examined and compared.

Il seminario si terra' presso la sede di Prometeia a Bologna in Via Marconi 43.