Seminario Dottorato: Robustness for path-dependent volatility models

Wednesday 6 April 2011 - Mauro Rosestolato

ARGOMENTI: Seminars Ph.D. Program

Wednesday 6 April 2011 h. 14:30, room 2BC30
Mauro Rosestolato (Pisa - SNS)
"Robustness for path-dependent volatility models"

In this introductory talk, we present a 2-dimensional market model in which only one component (say S) is observable in the market, while the other one (say P) is not observable, thus the choice of the starting point (S(0), P(0)) is a-priori subject to an error. This is the reason why we are interested firstly in investigating the dependence of the (S,P)-dynamics with respect to the initial condition, secondly in choosing an initial condition which minimizes the error.
The first issue is classical even in the deterministic case. The most intuitive and general approach is to recur to estimates based on Gromwall lemma, while if one instead uses the differentiability with respect to the initial conditions such estimates can be significantly improved. We will review this in the case of ordinary differential equations and see how the results generalize to the current case and how this improvement makes the model applicable in reality.
The second issue is treated by techniques based on invariant measures and the clever use of past observations: we will show that, by using the estimates based on the differentiability with respect to the initial conditions, the width of the past window required is linear with respect to the future time horizon.
Finally, we present some numerical results.

Rif. int. C. Marastoni, T. Vargiolu

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