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Three electricity spot price models: Evidence from PJM and Alberta markets

“Lunch at the Lab” Presentation Matt Lyle Department of mathematics&statistics University of Calgary, Alberta. Three electricity spot price models: Evidence from PJM and Alberta markets. Outline. Why these models? The random variable model The MR with Lapalcian motion and jumps model

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Three electricity spot price models: Evidence from PJM and Alberta markets

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  1. “Lunch at the Lab” Presentation Matt Lyle Department of mathematics&statistics University of Calgary, Alberta Three electricity spot price models: Evidence from PJM and Alberta markets

  2. Outline • Why these models? • The random variable model • The MR with Lapalcian motion and jumps model • The MR with many jumps model • Simulation results

  3. Why these models? • Standard models often overlook the unique characteristics seen in the electricity markets • They capture more of the statistical characteristics of electricity price paths • They are a result of the analysis found using the FFT method introduced last week

  4. The random variable model • Let us suppose the log spot price is as follows

  5. The random variable model • Let Where is the Noise component is the Jump component

  6. The random variable model • We would like to be able to model directly, but we really have two components • We use the recursive method suggested by Clewlow and Strickland to remove the jumps from the noise. • This will allow us to establish the distribution for the noise…

  7. The random variable model • The remaining noise after applying the recursive filter (anything greater then 3 std) for PJM

  8. The random variable model • The remaining noise after applying the recursive filter (anything greater then 3 std) for Alberta

  9. The random variable model • The density of the noise (the fit is logistic) PJM

  10. The random variable model • The density of the noise (the fit is logistic) Alberta

  11. The random variable model • We now have

  12. MR with Laplacian motion and jumps • Since Brownian motion does not capture the statistical characteristics in energy markets perhaps an other type will…

  13. MR with Laplacian motion and jumps

  14. MR with Laplacian motion and jumps

  15. The MR with many jumps model • Similar to the standard MR jump diffusion models we simply increase the number of jumps. • The idea comes from the Laplace distribution, which is similar to two exponential distributions spliced back-to-back

  16. The MR with many jumps model • So we get the following model

  17. Results: random variable model

  18. Results: random variable model

  19. Results: random variable model

  20. Results: MR with Laplacian motion

  21. Results: MR with Laplacian motion

  22. Results: MR with Laplacian motion

  23. Results: MR with many jumps

  24. Results: MR with many jumps

  25. Thank you • mrlyle@math.ucalgary.ca

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