Onyango-Otieno, Vitalis(University of Dundee, November , 1980)
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Abstract:
This thesis is essentially concerned with the connections between the classical orthogonal polynomials and the differential operators associated with the differential equations of Gegenbauer, Legendre, Laguerre and Hermite
Mutinda, Mary Wanza(University of Manchester, 2009)
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Abstract:
This paper presents an empirical analysis of a hybrid model for capturing the dynamics of the spot prices of electricity, and contingent claims thereof. The dynamics of the spot price process are captured as a sum of a deterministic price-demand transform and an Ornstein-Uhlenbeck stochastic component. From the tests on stability of parameters and recovery of the price process for in-sample and out-of-sample data, the model is shown to perform well. Closed form formulas for forward contracts are also presented using the market price of risk arguments. The parameter for market price of risk, λ , is estimated based on the convergence assumption i.e. the forward prices converge to the spot price experienced for the given future time. The estimated λ however fails the stability test indicating statistically significant changes in the value over time. In particular λ shifts from the expected negative value in seasons of high demand and variability (winter and summer) to indicate a value attached by the market for holding the forward contract; to positive values in low demand and variability seasons (spring and autumn) to indicate an net cost for holding the forward contract given the difficulty in storability of electricity relative to the almost assured production to meet demand. A discussion is also presented on the model performance as compared with other models defined for the UK market.