This thesis empirically evaluates a geometric Brownian motion and a stochastic volatility model for modeling futures prices and hedging Asian call options on the electricity spot price. Estimation of parameters for the models is done based on historical futures prices of futures contracts with a one month delivery period using nonlinear regression and Maximum Likelihood techniques. The models are tested on 2014 data and tracking error for each model is presented. The tracking error is investigated through the median value, the spread between minimum and maximum value along with value at risk at a 95% level. In addition, a third model for modeling spot and futures prices is presented theoretically. It is an exponential additive model with the advantage that it models the future price process from the spot price, instead of modeling the future price process immediately. This bypasses the issue of no information about the future price process during the delivery period, when there is no prices of the futures contracts. The aim of this thesis is to compare the simpler geometric Brownian motion to the more complex stochastic volatility model. It is found that the stochastic volatility model performs better when tested on out-of-sample data. The geometric Brownian motion tends to underestimate the electricity prices, despite that 2014 had low pricest compared to the other years in the data sample. In addition, the approximation of the distribution of the future price process under the geometric Brownian motion model gave a bad fit and led to difficulties when estimating the parameters. The stochastic volatility model produced more stable results and gave a better fit for the distribution.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-168437 |
| Date | January 2015 |
| Creators | Zackrisson, Ella |
| Publisher | KTH, Matematisk statistik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | TRITA-MAT-E ; 2015:28 |
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