Research

The research ground I’m developing during my post-doc, in continuity with my PhD, is probability theory applied to financial derivative modeling, pricing and hedging.

Within the classic risk neutral valuation framework I investigate the pricing and hedging problem of exotic contingent claims jointly depending on an asset performance at maturity and the overall volatility shown over the whole duration of the contract. A benchmark product of such kind is the target volatility option, a version of the classic call option, normalized with the realized volatility of the underlying. The rationale behind a TVO is to be able to take a position in a call option when the implied market volatility levels are excessively high, or to take advantage of a particular realized volatility view.

I am looking at such products under a great variety of stochastic models for the underlying; continuous stochastic volatility models, Lévy processes and most prominently stochastically time-changed Lévy processes. The introduction of time changes in the asset price Lévy model allows a unitary general valuation theory for models coming apparently from different areas of stochastic modeling. Motivated by this, I am interested in understanding to what extent tochastic processes can be looked at as being of time-changed type, which has eventually turned into a major aspect of my research. In my work I have introduced a class of time-changed stochastic processes suitable for financial uses which I called “decoupled time-changed processes”.  Such a class represents a useful generalization, in that it both includes all of the ordinary time-changed models and allows for a time-changed representation of some other existing models previously not classifiable as being of time-changed Lévy type.

My previous studies in algebraic geometry at BSc and MSc level where finalised by two dissertations. The first one is a short essay on the intersection form on projective surfaces and the resolution of bi-rational mappings between these in sequences of blow-ups. The second is a detailed study of an original paper by J.P. Serre containing the proof of his celebrated Duality Theorem in the case of (not necessarily compact) n-dimensional analytic complex manifolds.