*Tid:***7 april 2003 kl 1615-1700 **

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

*Föredragshållare:***
Mårten Grebäck
**

**Titel:** **
An Analytic Framework for Computing Value-at-Risk in Incomplete
Markets with Credit Risk. (Examensarbete)
**

**Sammanfattning:**

This master thesis presents a framework for analytic computation of Value-at-Risk for a portfolio of arbitrary derivatives. The underlying securities are modelled by jump-diffusion processes, where the number of jumps are Poisson distributed and the diffusion processes are driven by Brownian motions. The method is based on a delta-gamma approximation of the portfolio value and Fourier inversion of the characteristic function. In the second half of the thesis credit risk is introduced by a default event indicator variable. In case of a default, a certain fraction of the defaulted option's value is subtracted from the portfolio value. Several examples are presented illustrating the effects on Value-at-Risk with this extension.