Dear Colleagues,
We would like to invite
you to the following (double) SPASS seminar, jointly organized by UniPi,
SNS, UniFi and UniSi (abstracts below):
Signature-based models: theory and calibration
by Sara Svaluto Ferro (Università di Verona)
Noise-induced oscillations for the mean-field dissipative contact process
by Elisa Marini (Università degli Studi di Padova)
The seminars will take place on TUE, 4.6.2024 respectively at 14:00 CET in Aula Seminari, Dipartimento di Matematica, UNIPI and 15:00 CET in Aula Tricerri, Dipartimento di Matematica e Informatica "Ulisse Dini", UNIFI
and both streamed online at this link.
The organizers,
A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco
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Signature-based models: theory and calibration Abstract:
Universal classes of dynamic processes based on neural networks and
signature methods have recently entered the area of stochastic modeling
and Mathematical Finance. This has opened the door to robust and more
data-driven model selection mechanisms, while first principles like no
arbitrage still apply.
In the first part of the talk we focus on
signature SDEs whose characteristics are linear functions of a primary
underlying process, which can range from a (market-inferred) Brownian
motion to a general multidimensional tractable stochastic process. The
framework is universal in the sense that classical models can be
approximated arbitrarily well and that the model characteristics can be
learned from all sources of available data by simple methods. Indeed, we
derive formulas for the expected signature in terms of the expected
signature of the primary underlying process.
In the second part we
focus on a stochastic volatility model where the dynamics of the
volatility are described by linear functions of the (time extended)
signature of a primary process. Under the additional assumption that
this primary process is of polynomial type, we obtain closed form
expressions for the squared VIX by exploiting the fact that the
truncated signature of a polynomial process is again a polynomial
process. Adding to such a primary process the Brownian motion driving
the stock price, allows then to express both the log-price and the
squared VIX as linear functions of the signature of the corresponding
augmented process. For both SPX and VIX options we obtain highly
accurate calibration results.
The talk is based on joint works with Christa Cuchiero, Guido Gazzani, and Janka Möller.Noise-induced oscillations for the mean-field dissipative contact process
Abstract:
In this talk, we will introduce a dissipative version of the contact
process with mean-field interaction admitting a simple epidemiological
interpretation. In particular, we will focus on the thermodynamic limit
of the process, providing a law of large numbers (propagation of chaos)
and a central limit theorem for the corresponding normal fluctuations.
These
results reveal that it is the noise, which is only present in the
finite-size system and is internal to the system, that induces
persistent oscillatory behaviors reminiscent of the emergence of
pandemic waves in real epidemics.