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.