Browsing by Author "Lyle, Matthew R."

Now showing 1 - 4 of 4
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    Essays on continuous time finance
    (2009) Lyle, Matthew R.; Elliott, Robert J.
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    A model for energy pricing with stochastic emission costs
    (Elsevier, 2010) Elliott, Robert; Lyle, Matthew R.; Miao, Hong
    We use a supply-demand approach to value energy products exposed to emission cost uncertainty. We find closed form solutions for a number of popularly traded energy derivatives such as: forwards, European call options written on spot prices and European Call options written on forward contracts. Our modeling approach is to first construct noisy supply and demand processes and then equate them to find an equilibrium price. This approach is very general while still allowing for sensitivity analysis within a valuation setting. Our assumption is that, in the presence of emission costs, traditional supply growth will slow down causing output prices of energy products to become more costly over time. However, emission costs do not immediately cause output price appreciation, but instead expose individual projects, particularly those with high emission outputs, to much more extreme risks through the cost side of their profit stream. Our results have implications for hedging and pricing for producers operating in areas facing a stochastic emission cost environment.
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    A ‘simple’ hybrid model for power derivatives
    (Elsevier, 2009) Elliott, Robert; Lyle, Matthew R.
    This paper presents a method for valuing power derivatives using a supply–demand approach. Our method extends work in the field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices written on average spot prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black–Scholes equation. The model provides a relatively simple approach to describe the complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing.
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    The decomposition of electricity spot prices: a study of the Alberta and Pennsylvania, New Jersey, and Maryland power markets
    (2007) Lyle, Matthew R.; Swishchuk, Anatoliy
    This thesis is a study of the stochastic characteristics exhibited in the Alberta and Pennsylvania, New Jersey, and Maryland (P JM) power markets. Since electricity spot prices are notoriously difficult to model, we have developed a method which breaks the price into a stochastic or noise component and a deterministic component. This simplifies the complexity of modeling and allows for a richer study of each component. We present a robust method using the fast Fourier transform (FFT) for removing deterministic cycles from the spot price data. This allows for the study of the actual stochastic component within the data. Three models are then proposed for modeling the stochastic component of the de-cycled data. One of these models is in the form of a stochastic differential equation (SDE) which includes mean­reverting behaviour. The second is again mean-reverting but it also includes jumps. For both of these SDEs we were able to formulate a method to obtain a solution to the characteristic function and thus can obtain the density function, which is particularly helpful when working with non-standard models. The third model is a non-differential equation that uses random variables to model the spot price of electricity. Each of these models are then tested using real hourly spot market data from the Alberta and PJM markets for January 1, 2002 to December 31, 2005.