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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: A generalized Dupire formula and a stable way to estimate it

Workshop: Concluding Workshop

Time: Tue, December 02, 2008, 15:30-16:00

Speaker: Philipp Mayer

Abstract

Exponential Levy models are known to be capable of reproducing observed implied
volatility surfaces well for one maturity, but to have some problems when a
whole range of maturities shall be fitted. One way to overcome this drawback and
to introduce more flexibility in the model is by allowing for a state and time
dependent time change of the driving stochastic process. In the classic model of
Black and Scholes this procedure leads to the well-known local volatility model.
Now in order to calibrate the market model to the implied volatility surface one
needs to compute the time-change, which for the local volatility model can be
done using the famous Dupire formula. In this talk we consider the problem of
identifying the time change in a more general Levy market setting and derive a
Dupire-like formula for the generalized model. As in the local volatility
framework the formula is not stable in presence of data noise and we propose a
possible method to robustify its estimation.

Presentation slides (pdf, 333 KB)

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