Disputas: Asma Khedher

M.Sc. Asma Khedher ved Matematisk institutt vil forsvare sin avhandling for graden PhD: Sensitivity and Robustness to Model Risk in Lévy and Jump-Diffusion Setting

Asma Khedher

Tid og sted for prøveforelesning

10:15 Aud 1, Kristine Bonnevies hus: Quadratic hedging strategies

Bedømmelseskomité

  • Professor Michèle Vanmaele, Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent
  • Associate professor Friedrich Hubalek, Financial and Actuarial Mathematics, Vienna University of Technology
  • Professor Bernt Øksendal, Centre of Mathematics for Applications, Univesitetet i Oslo

Leder av disputas

Professor Tom Lindstrøm

Veiledere

  • Førsteamanuensis Giulia Di Nunno
  • Professor Fred Espen Benth
     

Sammendrag

The models that describe the financial market rely on many choices. The structure of the model, the interpretation of uncertainty, and the number and type of parameters included. Different traders may have different perceptions of the market data and modelling. Recently, the dynamics of asset prices seem to be well modelled by Lévy noise and most of current research in mathematical finance is focused around this class. These models generalize the classical continuous type models based on the Brownian motion to include possible jumps of the market prices. The jumps may also be of infinitely small size and occur with high intensity. Furthermore, it is a philosophical question whether asset prices are driven by pure-jump noise, or if there is a diffusion in the non-Gaussian dynamics. From a statistical point of view it may be very hard to determine whether a model should have a diffusion term or not.

In this thesis we consider the problem of robustness of the option price and the sensitivity parameters to model choice. Considering exponential Lévy models, we prove the robustness of option price after a change of measure. The measures that we considered are selected among the most popular choices of risk neutral equivalent martingale measures.Moreover, we prove the robustness of the sensitivity parameter delta of options written in such models. Dealing with Lévy models, we introduce the conditional density method. The latter provides the existence of a density of an independent variable in the underlying model. We also derive expressions for the delta of options written in a general jump-diffusion model using the Malliavin calculus. We apply our methods for the computation of the delta to power and commodity market models as well as to stochastic volatility models and we illustrate our results with several numerical examples.

For mer informasjon

Kontakt Marie Wennesland
 

Publisert 10. juni 2011 14:03 - Sist endret 28. nov. 2011 13:41