Seminari di Probabilità e Finanza Matematica: Price and volatility co-jumps

Martedì 19 Marzo 2013 ore 10:00 - Aula 1BC50 - R. Renò, F. Gozzi, E. Edoli


Seminari di Probabilità e Finanza Matematica

Martedì 19 marzo in aula 1BC/50 si terranno i seguenti seminari:

Ore 10:00
Roberto Renò
"Price and volatility co-jumps"

The dependence between the magnitudes of discontinuous changes in asset prices and contemporaneous discontinuous changes in volatility (co-jumps) is a fundamental aspect of the price process contributing, among other effects, to skewness in the return distribution. Yet, its nature has been reported by many as being - in terms of sign, magnitude, and statistical significance - largely elusive. Using a novel identification strategy for stochastic volatility modelling in continuous time relying on trade-level information for spot variance estimation, as well as infinitesimal cross-moments, this paper
documents that a sizeable proportion of discontinuous changes in asset prices are associated with strongly anti-correlated, contemporaneous changes in volatility. Not only are the price jump sizes strongly negatively correlated with the volatility jump sizes, but the absolute values of their (negative) mean and dispersion appear to increase with the volatility level, an additional effect which should lead to care in the management of joint directional and volatility jump risk.

Ore 11:00
Fausto Gozzi
"HJB equations for the Optimal Control of Dynamical Systems with Delay"

In this talk we first present some applied examples (coming from Economics and Finance) of Optimal Control Problems for Dynamical Systems with Delay (deterministic and stochastic). To treat such problems with the so called Dynamic Programming Approach one has to study a class of infinite dimensional HJB equations for which the existing theory does not apply due to their specific features (presence of state constraints, presence of first order differential operators in the state equation, possible unboundedness of the control operator). We will present some results on the existence of regular solutions for such equations and on existence of optimal control in feedback form.

Ore 11:45
Enrico Edoli will present his Ph.D. Thesis
"Pricing of gas swing contracts with indexed strike: a viscosity solution approach with applications"
(supervisor: Tiziano Vargiolu)