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Notes
- 1.
Through subsidies or quotas, see, for example, Jaromir et al. (2012).
- 2.
For more details on the history of Brownian motion in finance, the reader will find extensive literature. The book of Mandelbrot (2004) provides an elegant discussion.
- 3.
For the unfamiliar reader, the GBM is the reference model to the Black and Scholes (1973) option price formula.
- 4.
- 5.
We treat \( J \) as the absolute price jump. The relative price change is then treated as \( d{S_t}/{S_t}=(J{S_t}-{S_t})/{S_t}={J_t}-1 \).
- 6.
The difference is in the quality: the less sulfur, the easier it is to refine the crude into gasoline.
- 7.
Source: Bloomberg Energy.
- 8.
Practically, the first instance was due to the closure of the refinery, while the second owes to the unrest in Lybia.
- 9.
Since we are using a mean-reverting jump-diffusion model in our analysis, we also perform the tests over the periods we use to calibrate model parameters for every of our runs. We discuss this further in the text.
- 10.
To save space, we have not included our first estimation windows that start on 3 January 2001 and use the previous 12 months to estimate model parameters.
- 11.
The inverse leverage effect is usually observed in agricultural commodities.
- 12.
We note to the reader that the errors for so long-term forecasts the errors are substantially high.
- 13.
It is out of the scope of this chapter to propose the methodology for switching between models.
- 14.
Dan Morris, Global Strategist at J.P. Morgan Asset Management (in March 2012).
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Skindilias, K., Lo, C.C. (2013). Energy Security: Stochastic Analysis of Oil Prices. In: Leal Filho, W., Voudouris, V. (eds) Global Energy Policy and Security. Lecture Notes in Energy, vol 16. Springer, London. https://doi.org/10.1007/978-1-4471-5286-6_10
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