University of Padova, Department of Mathematics "Tullio Levi-Civita"
29 April 2021, ONLINE MEETING ON ZOOM
The second edition of the Spring Colloquium on Probability and Finance will bring together researchers working in stochastic analysis and mathematical finance. The workshop will feature five invited talks and attendance is open.
Organisers: Giorgia Callegaro and Claudio Fontana
To attend the Colloquium, please register by sending an e-mail to the organisers. You will receive the Zoom link and password in due time. In person participation is possible for a limited number of participants: if you are interested, please contact the organisers. Contact e-mail: fontana(at)math.unipd.it
SPEAKERS:
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René AID (Paris Dauphine Universty, FR)
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Luciano CAMPI (University of Milan, IT)
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Alessandro GNOATTO (University of Verona, IT)
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Antoine JACQUIER (Imperial College London, UK)
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Barbara PACCHIAROTTI (University of Rome "Tor Vergata", IT)
SCIENTIFIC PROGRAM:
9.00: welcome address
9.10 - 9.50: R. Aïd - Optimal dynamic regulation of carbon emissions market: a variational approach
Abstract: We consider the problem of reducing the carbon emissions of a set of firms over a finite horizon. A regulator dynamically allocates emission allowances to each firm. Firms face idiosyncratic as well as common economic shocks on emissions, and have linear quadratic abatement costs. Firms can trade allowances so to minimise total expected costs, from abatement and trading plus a quadratic terminal penalty. Using variational methods, we exhibit in closed-form the market equilibrium in function of regulator's dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. Again, we obtain a closed-form expression of the dynamic allocation policies that allow a desired expected emission reduction. Optimal policies are not unique but share common properties. Surprisingly, all optimal policies induce a constant abatement effort and a constant price of allowances. Dynamic allocations outperform static ones because of adjustment costs and uncertainty, in particular given the presence of common shocks. Our results are robust to some extensions, like risk aversion of firms or different penalty functions. Based on joint work with S. Biagini.
9.50 - 10.30: A. Jacquier - Looking at the smile from Roger Lee's shoulders
Abstract: looking at implied volatility surfaces from afar may not seem informative at first, but staring at them closely turns out to reveal a lot of information about the underlying stock price process. The objective of this talk is to gather as much information as possible about the stock, in particular: - is it a martingale or a strict local martingale? - can it default? - does it have fat tails? Starting from the foundational "Moment Formula" by Roger Lee, excavated about 15 years ago, we shall see how to squeeze even more information out of it and show how to develop pricing formulae for European option prices and variance swaps. We shall also investigate, time permitting, whether it is possible to move this volatility surface dynamically without introducing any kind of arbitrage.
10.30 - 11.00: break
11.00 - 11.40: A. Gnoatto - Cross currency valuation and hedging in the multiple curve framework
Abstract: we generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral. After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions. Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations. Based on joint work with N. Seiffert.
11.40 - 12.20: L. Campi - Mean-field games of finite-fuel capacity expansion with singular controls
Abstract: We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space in action and inaction region. We then show that a solution of the MFG of capacity expansion induces approximate Nash equilibria for the $N$-player games with approximation error $\varepsilon$ going to zero as $N$ tends to infinity. Our analysis relies entirely on probabilistic methods and extends the well-known connection between singular stochastic control and optimal stopping to a mean-field framework. Based on joint work with T. De Angelis, M. Ghio and G. Livieri.
12.20 - 13.00: B. Pacchiarotti - Short time asymptotics for log-modulated rough stochastic volatility models
Abstract: we establish a small time large deviation principle for log-price processes when the volatility is a function of a Gaussian Log-Modulated process. We also deduce short time asymptotics for implied volatility and for pricing. Based on joint work with P. Pigato.