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Adaptive Filtering in Electricity Spot Price Models
Shin Ichi Aihara
1
and Arunabha Bagchi
2
1
Department of Computer Media, Tokyo University of Science Suwa, 5000-1 Toyohira, Chino, Nagano, Japan
2
Department of Applied Mathematics, Twente University, P.O.Box 217, 7500AE, Ensched, The Netherlands
Keywords:
Electricity Spot, Risk premium, Hyperbolic system, Kalman filter, Jump process, Parameter identification,
Parallel filter.
Abstract:
We study the adaptive filtering for risk premium and system parameters in electricity futures modes. Introduc-
ing the jump augmented Vasicek model as the spot price mode, the factor model of the electricity futures is
constructed as the stochastic hyperbolic systems with jumps. Representing the main spike phenomena of the
electricity spot price from one observed futures data by proxy, the filtering of the stochastic risk premium and
its system parameters are developed in a Gaussian framework. By using the parallel filtering algorithm, the
online system parameter estimation procedure is proposed.
1 INTRODUCTION
It is well known that the electricity is quoted same
as any other commodity, e.g. crude oil, gold, copper
and others. As shown in Fig. 1, the electricity spot
prices present a higher volatility than equity prices
and its mathematical model is required for pricing of
electricity-related options, risk management and oth-
ers.
The peculiar characteristic of electricity is that one
can not store electricity, but there are many other char-
acteristics which distinguish electricity from other
commodities.
From Fig. 1, in which the spot price (a day-ahead
market) is shown, we observe the special behaviors
of electricity spot, i.e., many spikes frequently and
seasonal effect.
0 50 100 150 200 250 300 350
15
20
25
30
35
40
45
50
55
60
Time (day from 01/01/2013 to 31/12/2013)
Nord pool spot (EUR/MWh)
Figure 1: Nord Pool electricity spot price (day ahead im-
plicit auction market).
In this paper, instead of modeling this process
from the basic principle of supply and demand, the
simple mathematical model for this spot price is pro-
posed and leads to calibrate the model parameters
and price the options by using the stochastic sys-
tem approach. Along this line Schwartz and Smith
(Schwartz and Smith, 2000) proposed a two-factor
diffusion model and the system parameters are esti-
mated from M.L.E. (Maximum likelihood estimate)
by using Kalman filter. To apply this method one need
to add ad hoc observation noise in order to derive the
Kalman filter. This assumption has been made by nu-
merous authors, either in the commodity or interest
rate markets. The additional noise in the observa-
tion has been interpreted to bring into account bid-ask
spread, price limits or errors in the information. The
argument is clearly forced and unconvincing. By us-
ing the idea proposed by (Aihara and Bagchi, 2010),
we approach the modeling differently. In our setup,
on the one hand, the added measurement noise is
built in the model. On the other hand, the model-
ing of the correlation structure between the futures
(observation) is a natural component of our formu-
lation. Hence the model parameters can be calibrated
through the derived likelihood functional without any
ad hoc observation noise.
All the same, in these works, the important spikes
in the electricity prices could not be admitted, because
including jumps
1
means giving up on the closed-form
estimator like Kalman filter in (van Schuppen, 1977).
1
The closed-form formulae for forwards and options are
620
Aihara S. and BAGCHI A..
Adaptive Filtering in Electricity Spot Price Models.
DOI: 10.5220/0005014206200628
In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 620-628
ISBN: 978-989-758-039-0
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)