The time-frequency relationship between spot and futures prices of crude oil

• Thesis title in Czech: Časově-frekvenční vztah mezi spotovými a termínovanými cenami ropy
• Thesis title in English: The time-frequency relationship between spot and futures prices of crude oil
• Key words: Waveletová transformace, Vzájemné pohyby, Ropa, Termínový trh
• English key words: Wavelet tranformation, Comovement, Crude Oil, Futures market
• Academic year of topic announcement: 2014/2015
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Institute of Economic Studies (23-IES)
• Supervisor: doc. PhDr. Jozef Baruník, Ph.D.
• Author: hidden - assigned by the advisor
• Date of registration: 13.04.2015
• Date of assignment: 13.04.2015
• Date and time of defence: 10.02.2016 00:00
• Venue of defence: IES
• Date of electronic submission: 04.01.2016
• Date of proceeded defence: 10.02.2016
• Opponents: RNDr. Michal Červinka, Ph.D.

References

1. Keynes, J. M.: 1930, A Treatise on Money, Volume II,,London: MacMillan
2. Modest, D. M. and Sundaresan, M. (1983), The relationship between spot and futures prices in stock index futures markets: Some preliminary evidence. Journal of Futures Markets, 3: 15-41. Gorton, G. and Rouwenhorst, K. G.: 2006, Facts and fantasies about commodity futures, Financial Analysts Journal 62, 47-68.
3. Moosa, I. A. and Al-Loughani, N. E.: 1994, Unbiasedness and time varying risk premia in the crude oil futures market, Energy Economics 16, 99-105.
4. Barunik, J., & Barunikova, M., 2012. Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression, eprint arXiv:1208.4831 [q-fin.ST].
5. Fattouh, B. (2011). An Anatomy of the Crude Oil Pricing System. University of Oxford, Oxford Institute for Energy Studies. Oxford Institute for Energy Studies.
6. CME Group. (2013). Light Sweet Crude Oil (WTI) Futures and Options. Retrieved April 2014, from CME Group Inc. : www.cmegroup.com/trading/energy/files/en- 153 wti brochure sr.pdf
7. Silvapulle, P., and Moosa, I.A., 1999. The Relationship between Spot and Futures Prices: Evidence from the Cruide Oil Market. The Journal of Futures Markets 19, 175-193.
8. Bopp, A. E., and Sitzer, S., 1987. Are petroleum futures prices good predictors of cash value? The Journal of Futures Markets 7, 705-719.
9. Ludlow,J.& Enders,W.(2000).Estimatingnon-linear ARMA models using Fourier co- efficients. International Journal of Forecasting, 16(3), 333-347.
10. Harvey, A. C. & Jaeger, A. (1993). Detrending, stylized facts and the business cycle. Journal of applied econometrics, 8, 231-231.
11. Gallegati, M. (2012). A wavelet-based approach to test for financial market contagion., Computational Statistics & Data Analysis, 56(11), 3491-3497.
12. Littlewood, J. & Paley R. (1931) Theorems on Fourier series and power series. Journal of Lond. Math. Soc. 6:230/233 Ricker N. (1953) The form and laws of propagation of seismic wavelets. Geophysics 18(10)
13. GoupillaudP.,GrossmanA.&MorletJ.(1984)”Cycle-Octave and Related Transforms in Seismic Signal Analysis”. Geoexploration, 23:85-102
14. Addison, P. S. (2002). The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. CRC Press.
15. Torrence,C.& Compo,G.P.(1998).A practical guide to wavelet analysis.Bulletin of the American Meteorological society, 79(1), 61-78.
16. Heisenberg, W. (1928). Zur theorie des ferromagnetismus. Zeitschrift fur Physik, 49 (9-10), 619-636.
17. Aguiar-Conraria, L., Azavedo N. & Soares, M. J. (2008). Using wavelets to de- com- pose the time-frequency effects of monetary policy. Physica A: Statistical mechanics and its Applications, 387(12), 2863-2878.
18. Mallat, S. (1999). A wavelet tour of signal processing. Access Online via Elsevier.
19. Ramsey, J. & Thong, J. (2012). ”Time-Scale and the S-Curve: A Wavelet Analysis of
Trade Dynamics.” Available at SSRN 2146108 .
20. Percival, D., Mofjeld, H. O. (1997). Analysis of subtidal coastal sea level fluctuations
using wavelets. Journal of the American Statistical Association, 92(439), 868-880.
21. Kim, S. & F. In (2005): ”The relationship between stock returns and inflation: new
evidence from wavelet analysis.” Journal of Empirical Finance 12: pp. 435-440.
22. Haar, A.,(1910) Zur Theorie der orthogonalen Funktionensysteme, Math. Ann., 69 ,
331-371
23. GrinstedA.,Moore,J.C.&JevrejevaS.(2004),Applicationofthecrosswavelettrans- form and wavelet coherence to geophysical time series, Nonlin. Processes Geophys., 11, 561-566

Preliminary scope of work in English

In this thesis I want to investigate the relationship between daily spot and futures prices for maturities of one, two, three and four months of West Texas Intermediate (WTI) crude oil. I will use the data that cover periods January 1987-April 2015. Based on economic theory, the forward prices should be closely related to the spot price, which - in the case of crude oil - I will try to confirm using wavelet-based approach. Main contributions of this thesis will be the findings in the field of time-frequency relationship of spot-futures prices in crude oil market where an alternative methodology - wavelet transformation - will be used. The usage of this advanced method is also an additional contribution for the thesis because it allows to rigorously study how co-movement differs across frequencies/scales and time. In this thesis I will use wavelet Coherence as well as wavelet bivariate correlation. My aim in this thesis is to show that co-movement is significant in all scales unlike other commodities like gasoline where co-movement is strong mainly in higher scales. However according to (Keynes 1930) who claims that if the futures price contains a risk premium, then it will be biased expectation of future spot prices. Hence in this thesis I want also to examines ex-post futures premiums.The novelty of this thesis will be a computation of risk premium on significant scales using Wavelet band spectral regression (WBLS).