Dear all,

Prof. Elisa Alos (Universitat Pompeu Fabra) will hold the two following Seminars.

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On Tuesday, 27 March 2018 — at 11:00 — Room: Aula Fermi: Title : The implied volatility surface in modeling problems

Abstract:

In the Black-Scholes model, the volatility parameter is constant. But it is well-known that, if we compute this volatility parameter by inverting market option prices, the result (the implied volatility) will depend on the strike price (a variation described graphically as a smile or skew) and on time to maturity. Classical stochastic volatility models, where the volatility is allowed to be a diffusion process, can capture the observed smiles and skews, but they cannot easily explain the term structure. For instance, recent numerical analysis state that the skew slope is approximately $O((T )^{-k})$, for some positive $k$ and where $T$ denotes the time to maturity, while the rate for these stochastic volatility models is $O(1)$. In this talk, we will see how to construct new stochastic volatility models that can describe this phenomena. Towards this end, we will present short-time approximations for the implied volatility skew and smile. The obtained formulas will give us a useful tool to identify the volatilities that can explain this term structure. Based on this approach, some new models have been proposed recently (as, for example, rough volatilities). In this talk we will discuss on the state of the art of this modeling research, and we will discuss the main advantages and disavantages of these new models.

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On Wednesday, 28 March 2018 — at 14:00 — Room: Aula Bianchi Scienze Title : On the link between the Malliavin derivative operator and the implied volatility behaviour

Abstract:

We use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew and smile, in the context of stochastic volatility models. Our analysis does not requiere the volatility to be a diffusion or a Markov process. The obtained results will give us a tool to construct new models that can allow us to explain the empirical term structure of the implied volatility surface (joint works with J. León and J. Vives).

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Fill free to forward this announcement to your colleagues.

Best

Giulia Livieri Assegnista di ricerca Scuola Normale Superiore Piazza dei Cavalieri, 7, 56126 Pisa PI room 65