*Tid:***19 september 2005 kl 1515-1600 **

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

*Föredragshållare:***
Carl Mikael Bergman
**

**Titel:** **
Estimating Volatility Structures for Pricing Options with
Electricity Forwards and Futures as Underlying Assets.
(Examensarbete)
**

* Sammanfattning: *
At Nord Pool options are traded with forward contracts on
electricity as the underlying asset. The market uses a constant,
implied volatility as input into the Black-76 formula for option
pricing. However, the assumption of a constant volatility is
clearly violated for forward prices at Nord Pool. The focus of this
thesis is on methods of specifying the volatility for forward and
futures contracts to allow for time dependence, which then can be
used for valuing options. Two different approaches are used; for
seasonal forwards, we propose a method where historical price data
are used to obtain time-varying variance functions, and for monthly
futures we apply principal components analysis to obtain the
volatility structure. Thereafter both approaches are used as input
into Black-76 to obtain option prices. Interestingly, we find that
forward and futures seem to exhibit different volatility dynamics;
forward prices seem to be more volatile than futures prices towards
delivery. For seasonal forwards, we can compare our own option
prices with real option prices from Nord Pool, and for monthly
futures, we obtain theoretical option prices by using the results
of the principal components analysis.