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<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration:underline"><span style="font-size:18pt;font-family:"Times New Roman",serif">SEMINARIO
DI FINANZA QUANTITATIVA<span></span></span></p>

<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration:underline"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span><span style="text-decoration:none"> </span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">martedì <span> </span>27 marzo 2018</span><span style="font-size:16pt;font-family:"Times New Roman",serif"><span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">ore <span>11:00</span><span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><u><span style="font-size:16pt;font-family:"Times New Roman",serif">Scuola Normale Superiore<span></span></span></u></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Pisa<span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white">Aula Fermi<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><u><span style="font-size:16pt;font-family:"Times New Roman",serif"><span><span style="text-decoration:none"> </span></span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span class="gmail-apple-converted-space"><b><span style="font-size:24pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white"> </span></b></span><b><span style="font-size:24pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white">Elisa Alos</span></b><b><span style="font-size:24pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">(<span style="background:white">Universitat Pompeu Fabra,
Barcellona</span></span>)<span></span></i></p>

<pre style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:10pt;font-family:"Courier New""><b><i><span style="font-size:12pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white"><span> </span></span></i></b></pre>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">terrà un
seminario dal titolo:<span></span></span></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif;color:black">“</span></b><strong><span lang="EN-US" style="font-size:20pt;color:rgb(34,34,34);background:white">The implied volatility surface in modeling problems</span></strong><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif;color:black">”</span></b><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif"><span> </span></span></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span style="font-family:"Times New Roman",serif">Abstract:<span></span></span></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-family:TradeGothicPl-CondEighteen"><i style=""><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white">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.</span></i><b style=""><i><span lang="EN-US" style="font-family:"Times New Roman",serif"><span></span></span></i></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif"> </span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Tutti gli interessati sono invitati a
partecipare.<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Classe di Scienze<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p><br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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