*Tid:***18 april 2005 kl 1615-1700 **

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

*Föredragshållare:***
Andreas Johansson.
**

**Titel:** **
Stochastic modelling of commodity prices with applications to
the German market.
(Examensarbete)
**

* Sammanfattning: *
This thesis describes some aspects of the stochastic behaviour of
commodity prices. We establish a connection between the price on
crude oil and electricity in the German market and implement
stochastic models for the price process of these two commodities.
First we implement a one-factor model according to Schwartz (1997)
in which the logarithm of the spot price follows an Ornstein-
Uhlenbeck process. Further, a variant of the Gibson and Schwartz
(1990) two-factor model suggested by Carmona and Ludkovski (2004) is
implemented where the spot price is modelled as a geometric Brownian
motion and the convenience yield as an Ornstein-Uhlenbeck process.
In this model the convenience yield enters the drift of the spot
price and introduces mean reversion in the spot price. We also
verify the hypothesis that the convenience yield is the net flow of
services that accrues to the holder of a physical commodity and show
that it can serve as an indicator of market transitions between
contango and backwardation.

A futures volatility model inspired by Blix (2003) is a different approach that is discussed where we try to fit the historical futures volatility term structure and from this retreive the futures price. The model accounts for the seasonality as well as the time to maturity effect in the futures price volatility, which also corresponds to mean reversion in the spot price.