Disputation: Marc Lagunas Merino
Doctoral candidate Marc Lagunas Merino at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is defending the thesis:
Stochastic Modeling with Fractional and non-Fractional Noises
Applications to Finance and Insurance
for the degree of Philosophiae Doctor.
Doctoral candidate Marc Lagunas Merino
The University of Oslo is closed. The PhD defence and trial lecture will therefore be digital 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.
- The webinar opens for participation just before the disputation starts, participants who join early will be put in a waiting room.
Tittle: "Local volatility models and Dupire’s formula."
Main research findings
In my doctoral work, I have developed stochastic models that use different type of noises, to price financial derivatives and insurance products.
Stock prices have a random component in their behavior that characterizes statistical aspects of that particular asset. The type of noise chosen to model the dynamics of prices is key to reproduce empirical facts of assets. In this dissertation I have developed the continuous version for a new kind of noise with memory. One of its particularities is that it takes into account all the past states, in order to determine its current state and smoothness. This is a highly desirable feature in asset modeling. I have also proposed a new approximating formula for call options in the form of a series expansion that can be truncated to any desired order depending on the degree of accuracy needed. A second approximating formula is also provided for the case where the noise used to model stock prices and volatility has discontinuous trajectories.
In the scope of a different project I have also proposed a model to price insurance products that takes into account the join risks arised from stock price volatility and interest rates.