Abstract
Multi-asset derivative pricing is still an active field of research in financial modeling, calling for multivariate stochastic models that reproduce well-known stylized facts such as skewness and excess kurtosis of marginal return distributions.
The objectives of this research project are to build stochastic models for financial assets, develop calibration procedures and simulation methods. Simulations are necessary to price derivatives if analytical pricing formulas are not available, and they are also necessary to generate future scenarios for out-of-sample evaluation.
A class of models widely used in finance are Markov processes. Among them, Lévy processes, which are characterized by independent and time-homogeneous increments, are widely used because of their analytical tractability and good fit on financial data. These processes are recently used to build multivariate models able to incorporate linear and non-linear dependencies among assets. In fact, both linear and non-linear dependence may affect the price of a multi-asset derivative or the risk associated with a financial position.
One of the objectives of the present project is to build and characterize multivariate stochastic processes able to reproduce well-known stylized facts and with a flexible dependence structure. A way to build multivariate stochastic models in finance is to subordinate a Lévy process or, more in general, a Markov process.
Subordination has the nice economic interpretation of a change of time. The underlying idea is that the time runs fast when there are a lot of orders, while it slows down when trade is stale. If both the processes are of Lèvy type the resulting process is also Lèvy, otherwise we introduce time inhomogeneity using more general change of time.
Once the model has been built the objective becomes to calibrate the models on real data, and evaluate its fit properties.
General Info
This PhD project is part of a call for 5 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science https://dottorato-mds.campusnet.unito.it/do/home.pl at the University of Turin (Italy). The call will open on 28 April 2022 (date TBC). The scholarship is for three years, starting in October 2022.
The PhD program is interdisciplinary, and it involves branches of mathematics, informatics, economics, statistics, and physics.
All interested candidates should submit their application online via the link https://www.phd.unito.it/do/home.pl/View?doc=Submitting_your_application.html. Deadline for applying is 30 May 2022 (date TBC). Notice that the application requires two reference letters, which should be submitted via the same link by the referees before the application deadline. The referees will be able to submit their letters only after the candidate has input all the required information and closed their (part of the) application. If the letters are not submitted by the deadline the application will not be valid.
For more information, do not hesitate to contact the supervisor. More information, including the official call and all relevant (confirmed) deadlines, can also be found here https://dottorato-mds.campusnet.unito.it/do/home.pl/View?doc=/content/Admission.html.
The call for applications is available at the page https://www.dottorato.unito.it/do/home.pl/View?doc=Bando_XXXVIII_ciclo.html.
Admission details and the list of projects can be found here https://www.dottorato.unito.it/do/documenti.pl/ShowFile?_id=g3ot;field=file;key=JbqgKqg0lroYaYMa8BXEFYBVz1z8MXSdAKr7fGFtPR2;t=3298.
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