The valuation of weather derivatives is greatly dependent on accurate modeling and forecasting of the underlying temperature indices. The complexity and uncertainty in such modeling has led to several temperature processes being developed for the Monte Carlo simulation of daily average temperatures. In this report, we aim to compare the results of two recently developed models by Gyamerah et al. (2018) and Evarest, Berntsson, Singull, and Yang (2018). The paper gives a thorough introduction to option theory, Lévy and Wiener processes, and generalized hyperbolic distributions frequently used in temperature modeling. Implementations of maximum likelihood estimation and the expectation-maximization algorithm with Kim's smoothed transition probabilities are used to fit the Lévy process distributions and both models' parameters, respectively. Later, the use of both models is considered for the pricing of European HDD and CDD options by Monte Carlo simulation. The evaluation shows a tendency toward the shifted temperature regime over the base regime, in contrast to the two articles, when evaluated for three data sets. Simulation is successfully demonstrated for the model of Evarest, however Gyamerah's model was unable to be replicated. This is concluded to be due to the two articles containing several incorrect derivations, why the thesis is left unanswered and the articles' conclusions are questioned. We end by proposing further validation of the two models and summarize the alterations required for a correct implementation.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-180411 |
| Date | January 2021 |
| Creators | Gerdin Börjesson, Fredrik |
| Publisher | Linköpings universitet, Tillämpad matematik, Linköpings universitet, Tekniska fakulteten |
| 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 |
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