*Tid:***28 maj 2007 kl 15.15-17.00 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Erik Lindström, Matematisk statistik, Universitetet i Lund.
**

* Titel: *
Implications of real world filtrations on valuation and calibration in
financial data.

* Sammanfattning: *
The first part of the seminar will analyze the valuation problem when
investors only have access to a finite sequence of observations. This is
the case for all real world applications.
It will be shown that values, derived using standard conditions, will be
stochastic and have to be treated as such. This problem is pronounced
under when stochastic volatility (or latent factor) models are used.
However, assuming that the agents are aware of this problem and that
they are using the best possible correction generates some interesting
stylized facts on the volatility structure which are consistent with the
observed option volatility structure.

In the second part of the talk deals with calibration of options prices data. Robust calibration of option valuation models to quoted option prices is nontrivial, but as important for good performance as the valuation model itself. The standard textbook approach to option calibration is minimization of a suitably chosen measure of the prediction error, e.g. least squares minimization. We interpret the total prediction error as a sum of the measurement errors and effects from the parameter dynamics, and postulate dynamics for the parameters. This will allow the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently.

We used the Heston, Bates and NIG-CIR models in this paper, applying the calibration methods on simulated data and data from the S&P-500. The general tendency is that the proposed method reduces the overfitting significantly compared to naive least squares estimation.

Based on joint work with Patrice Jabet, Mats Brodén, Jan Holst, Jonas Ströjby and Magnus Wiktorsson.