STAR-seminars: Stefano De Marco

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The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.

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Speaker: Stefano De Marco (CMAP, Ecole Polytechnique)

Title: On the implied and local volatility surfaces generated by rough volatility

Abstract: Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by such models, and supporting their calibration power to SP500 option data.

Rough volatility models also generate a local volatility surface, via the Markovian projection of the stochastic volatility (equivalently, via Dupire's formula applied to the model's option price surface). We complement the existing results with the asymptotic behavior of the local volatility surface generated by a class of rough stochastic volatility models encompassing the rough Bergomi model.

Notably, we observe that the celebrated "1/2 skew rule" linking the short-term at-the-money (ATM) skew of the implied volatility to the short-term ATM skew of the local volatility, a consequence of the celebrated "harmonic mean formula" of [Berestycki, Busca, and Florent, QF 2002], is replaced by a new rule: the ratio of the implied volatility and local volatility ATM skews tends to the constant 1/(H + 3/2) (as opposed to the constant 1/2), where H is the regularity index of the underlying instantaneous volatility process.

Joint work with  Florian Bourgey, Peter Friz, and Paolo Pigato.

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This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS

Published May 25, 2021 4:04 PM - Last modified Sep. 13, 2021 2:40 PM