This thesis studies the options traded at the Nordic power market Nord Pool, which are written on yearly and quarterly forward contracts. The most widely used pricing model at the market is Black 76, a model that assumes the options underlying variable to be log-normally distributed, and volatility to be constant over time. In order to examine whether these assumptions are true, we firstly perform normality tests for the spot, futures and forward log-returns. We find that neither of them follows a log-normal distribution, but also that the forward log-returns are much closer to being log-normally distributed than the other variables. Secondly, we examine the implied volatility smiles for traded options and the implied volatility term structure at Nord Pool. We find that different options trade at different volatility levels, especially as time to maturity decreases, and hence volatility is not constant over time. Our thesis concludes that there are benefits from using Black 76, but nonetheless are two important model assumptions violated.
Contents
1. INTRODUCTION
1.1 Objectives
1.2 Delimitations
1.3 Methodology and Structure
2. INSTITUTIONAL BACKGROUND
2.1 Nord Pool and Market Characteristics
2.2 Trading and Market Participants
2.2.1 Supply
2.2.2 Demand
2.3 The Spot Market
2.4 The Financial Electricity Market
2.4.1 Futures Contracts
2.4.2 Forward Contracts
2.4.3 Options
2.4.4 Other Contracts Traded at Nord Pool
3. THEORY
3.1 Forwards and Futures
3.2 Geometric Brownian Motion
3.3 Black 76
3.4 Volatility
4. BLACK 76 IN REALITY
5. SPOT, FUTURES AND FORWARD PRICES
5.1 Normal Distribution
5.2 Discussion of the Results
6. IMPLIED VOLATILITY
6.1 Implied Volatility Smile
6.2 Evolution of the Implied Volatility Smile
6.3 Implied Volatility Term Structure
7. CONCLUSION
7.1 Further Research
8. REFERENCES
9. APPENDIX 1 PRICE CURVES FORWARDS
10. APPENDIX 2 LOG-NORMAL DISTRIBUTION
11. APPENDIX 3 IMPLIED VOLATILITY SMILES
12. APPENDIX 4 EVOLUTION OF THE SMILES
13. APPENDIX 5 VOLATILITY TERM STRUCTURE
Author: Patricia Deyna,Maria Hultström
Source: Stockholm School of Economics