*Tid:***24 april 1998 kl 1515-1600** (Obs dagen!)

*Plats :***Seminarierummet 3721** (Obs platsen!), Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***Marc Bohlin.
** (Examensarbete)

**Titel:** **
Pricing of Options with Electricity Futures as Underlying Assets
**

**
Sammanfattning:
**
In this thesis we use stochastic calculus to theoretically price
electricity contingent claims (derivatives). The analysis is similar
to the one leading to
Black-Scholes'
formula for option pricing and
risk-free valuation.

Most contingent claims are dependent on an underlying asset. So, by finding a "reasonable" price process for the underlying asset, the prices of the different contingent claims are given by arbitrage arguments. But, electricity at the spot market cannot be stored, which leads to an incomplete market. Even though the main task in this thesis deals with the futures market, the situation at the spot market has to be taken into consideration. Therefore, price calculations have to rely on a different technique than the original Black-Scholes analysis. The main difference will be the need to estimate a parameter called the market price of risk.

First, we suggest a process for the spot price whose dynamics follows a mean reverting (Ornstein-Uhlenbeck) process. This process consists of a Wiener increment added to a deterministic function. The deterministic function is chosen to follow a model developed by the Norwegian Electric Power Research Institute (EFI). At Vattenfall, the EFI-model is used frequently and especially for production planning. By combining a stochastic process and the EFI-model, we end up with realistic dynamics for the spot price, and it allows us to price most contingent claims based on the spot price. Once the spot price has been specified, the transformation to the futures market can take place.

The model presented for the spot market has been transformed and tested for futures contracts traded by the Nord Pool, and the model turns out to be valid for the term structure at distinct points of time. The model gives a better correspondence to the observed market prices than the EFI-model. The model also gives us the possibility to estimate the market prices of risk at different points of time.