The PhD defence will be partially digital, in Abels Utsikt, 12th floor, Niels Henrik Abels hus and streamed directly using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.
Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence. If you would like to ask a question, click 'Raise hand' and wait to be unmuted.
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Join the disputation
The webinar opens for participation just before the disputation starts, participants who join early will be put in a waiting room. -
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Submit request to access (available from 2nd of December 13:15 until 16th of December 13:15)
Trial lecture
16th of December, time: 10:15 pm, Abels Utsikt, 12 etg. Niels Henrik Abels hus, and digitally on Zoom.
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Join the trial lecture
The webinar opens for participation just before the trial lecture starts, participants who join early will be put in a waiting room.
Main research findings
Financial markets have extremely complex behavior that cannot be fully modeled using classical approaches. In particular, numerous empirical studies show that market volatility exhibits some form of long-range dependence and has time-varying Hölder regularity with prominent periods of “roughness” (i.e. of Hölder order ≈0.1). These two properties are far beyond the capabilities of classical Brownian diffusions and it is challenging to reproduce them simultaneously in one model.
In the present thesis, we suggest a novel volatility modeling framework that grasps this unconventional behavior and solves a number of technical problems that are typical for classical stochastic volatility models. Namely, our model comprises the following properties:
- flexibility in the noise: the suggested model accepts various drivers – from fractional Brownian motions with different Hurst indices to general Hölder continuous processes – to account for different option pricing
phenomenons;
- control over the moments of the price: the model ensures the existence of moments of necessary orders for the corresponding price process;
- positivity: the volatility process is strictly positive and has inverse moments to ensure reasonable behavior of martingale densities.
We also present a variety of associated numerical methods and propose practically feasible algorithms for various applications, such as the pricing of contingent claims (including options with discontinuous payoffs) and mean-square hedging.
Adjudication committee
- Associate Professor Elisa Alòs, Universitat Pompeu Fabra
- Professor Saul D. Jacka, University of Warwick
- Professor Tom Lindstrøm, University of Oslo
Supervisors
- Professor Giulia Di Nunno, University of Oslo
- Professor Salvador Ortiz-Latorre, University of Oslo
- Professor Yuliya Mishura, Taras Shevchenko National University of Kyiv
Chair of defence
Professor Nils Henrik Risebro
Host of the session
Professor Tom Lindstrøm