Stohastično modeliranje cen električne energije na dnevnem trgu z uporabo Ornstein-Uhlenbeckovih procesov

diplomsko delo

Branko Knežević (Avtor), Dominik Benkovič (Mentor), Timotej Jagrič (Komentor)

Povzetek

V začetku devetdesetih let 20. stoletja je prišlo do deregulacije mnogih trgov električne energije po vsem svetu. Zaradi teh sprememb je električna energija postala tržno blago. Ta zaradi svojih omejitev v shranjevanju in transportu predstavlja edinstveno obliko blaga. To se kaže tudi v načinu, po katerem trgovanje z električno energijo poteka. Udeleženec lahko na trgu povprašuje po zelo različnih proizvodih. Med drugim trgovanje z električno energijo poteka na dnevnem trgu, na katerem udeleženci sklepajo pogodbe za dobavo neposredno v prihajajočem dnevu. Poznavanje gibanje cene električne energije na dnevnem trgu je za vsakega udeleženca na trgu zelo pomembno. V diplomskem delu je opisan način vrednotenja nestandardnih proizvodov, torej tistih s katerimi na borzah ni mogoče trgovati. Osnovna predpostavka takega vrednotenja je poznavanje dinamike cen na dnevnem trgu. Predstavljen je stohastičen model za modeliranje cen električne energije na dnevnem trgu. Še pred tem so opisane temeljne značilnosti teh cen, kot so trend, sezonskost, vračanje k srednji vrednosti, konice. Posebna značilnost teh cen je tudi avtokorelacijska funkcija, ki jo je mogoče zelo lepo opisati z linearno kombinacijo eksponentnih funkcij. V diplomskem delu predstavljen model temelji na Ornstein-Uhlenbeckovih procesih, v katerih naključna gibanja modeliramo z Brownovimi gibanji in semimartingali. Končen model je produkt multiplikativne sezonske funkcije in vsote dveh Ornstein-Uhlenbeckovih procesov, v katerih naključna gibanja povzročata Brownovo gibanje in sestavljen Poissonov proces. Predstavljena je metoda za filtriranje konic iz časovne vrste cen dnevnega trga, katere rezultat sta temeljni signal in signal konic. Iz teh signalov z metodami, ki so tudi predstavljene, ocenimo parametre modela. Matematično ozadje modela je predstavljeno v dodatkih A in B. Izkaže se, da se simulacije cen s takim modelom obnašajo podobno kot cene same glede na to, da se simulirane cene gibljejo v mejah kot realizirane cene. Pri tem je vredno poudariti, da v modelu kot fiksen parameter nastopa le en podatek o realizirani ceni. S takim modelom je mogoče modelirati dinamiko cen, ne pa jih tudi na dolgi rok napovedovati.

Ključne besede

električna energija;dnevni trg;cena;Ornstein-Uhlenbeckovi procesi;Brownovo gibanje;semimartingal;Poissonov proces;filtriranje;diplomska dela;

Podatki

Jezik:	Slovenski jezik
Leto izida:	2009
Izvor:	Maribor
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UM FNM - Fakulteta za naravoslovje in matematiko
Založnik:	[B. Knežević]
UDK:	51(043.2)
COBISS:	16990472
Št. ogledov:	3313
Št. prenosov:	270
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	STOCHASTIC MODELLING OF ELECTRICITY SPOT PRICES USING ORNSTEIN-UHLENBECK PROCESSES
Sekundarni povzetek:	Since the early nineties of the 20th century many electricity markets worldwide have experienced deregulation. Electricity has thus become a commodity. Electricity is because of its non-storeability and limitations in transport a unique commodity. This has a profound effect on the organization of the electricity markets. Participants in such markets are able to buy and sell very different products. They are able to make long-term contracks and are also able to trade in a spot market, where electricity is traded for the delivery in the next day. It is crucial for every market participant to understant the the dynamics of prices move in the spot market. In the diploma a methodology for pricing non-standard products, i.e. products which cannot be traded on the exchange, is presented. The main input for such pricing is the dynamics of electricity spot prices. A stochastic model is presented for modelling such prices. But before that main characteristics of electricity spot prices are presented. These are trend, seasonality, mean-reversion and spikes. A special feature of these prices is their autocorrelation function, which can be presented as a linear combination of exponent functions. The presented stochastic model is based on Ornstein-Uhlenbeck processes, in which random jumps are caused by Brownian motions and semimartingales. The final model is a product of multiplicative seasonal function and a sum of two Ornstein-Uhlenbeck processes, in which random jumps are caused by Brownian motion and a compound Poisson process. A method for filtering spikes from the deseasonalized spot price time series is presented. The result of such filtration are base and spike signals. Methods for model parameter estimatian from these signals are also presented. The mathematical background of the model is given in appendices A and B. The conclusion of the diploma is, that the presented model sumulates curves that behave in a similar way as the spot prices itself in the way, that the simulations mean-revert around the seasonal function and they stay within boundaries as the spot prices themselves. It is worth mentioning, that only one spot price from the initial time series is included in the model as paramater and ramains unchanged during the entire simulation. This simple model is a good starting point for modeling spot price dynamics, but is, as it is also shown, not suitable for long-term forecasting.
Sekundarne ključne besede:	spot market;spot price;Ornstein-Uhlenbeck processes;Brownian motion;semimartingale;compound Poisson process;filtration;
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Diplomsko delo
Komentar na gradivo:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Strani:	IX, 59 f.
Ključne besede (UDK):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	8761633