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Erratum to “When to drill? Trigger prices for the arctic national wildlife refuge” [Resour. Energy Econ. 27(4) (2005) 273–286]
Resource and Energy Economics 29 (2007) 244–245 www.elsevier.com/locate/ree
Erratum
Erratum to ‘‘When to drill? Trigger prices for the arctic national wildlife refuge’’ [Resour. Energy Econ. 27(4) (2005) 273–286] Jon M. Conrad *, Koji Kotani Cornell University, AEM, 455 Warren Hall, Ithaca, NY, 14853, United States Available online 17 June 2007
Two mistakes were made in calculating the standard deviation rates for the stochastic processes describing oil prices in our paper ‘‘When to Drill? Trigger Prices for the Arctic National Wildlife Refuge,’’ Resource and Energy Economics, 27(4) (2005) 273–286. These mistakes were brought to our attention by Professor Paul Fackler and we are indebted to him for pointing them out. (Professor Fackler has additional comments and concerns about our analysis. See his comment in this volume.) First, we mistakenly used the value of the variance instead of the standard deviation when calculating the trigger prices in the model with geometric Brownian motion (GBM). The correct value in this model should be s = 0.23. Second, we used an incorrect formula in calculating the standard deviation for the mean-reverting (M-R) process. The correct formula and value should be vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ˆ u 2 lnð1 þ bÞ 2ˆh sˆ ¼ sˆ e ¼ 6:3 ¼ sˆ e t ˆ 2 2 h ð1 e Þ ˆ 1 ½ð1 þ bÞ An increase in the standard deviation rate in either model will increase the trigger prices. This effect is quantitatively more pronounced in the GBM model. The corrected trigger prices for our base-case parameter set are given in the table below.
DOI of original article: 10.1016/j.reseneeco.2005.01.001. * Corresponding author. Tel.: +1 607 255 7681; fax: +1 607 255 9984. E-mail address: [email protected] (J.M. Conrad). 0928-7655/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.reseneeco.2007.06.002
Erratum / Resource and Energy Economics 29 (2007) 244–245
245
A (106)
P* GBM (g = h = 0, s = 0.23)
P* M-R (s = 6.3)
$ $ $ $ $ $ $ $ $ $ $
$ $ $ $ $ $ $ $ $ $ $
$ $ $ $ $ $ $ $ $ $ $
200 210 220 230 240 250 260 270 280 290 300
27.96 28.16 28.36 28.56 28.76 28.96 29.16 29.36 29.56 29.76 29.96
27.99 28.61 29.24 29.86 30.49 31.13 31.77 32.42 33.08 33.74 34.41
The corrected trigger prices now range from $ 27.96/bbl to $ 34.41/bbl. In the original paper, with the incorrect standard deviation rates, they ranged from $ 19.84/bbl to $ 31.42/bbl. Oil prices in mid-December, 2005, have ranged between $ 55/bbl and $ 60.00/bbl and would seem to justify exploration and development based on the corrected calibration of our current models.
Erratum
Erratum to ‘‘When to drill? Trigger prices for the arctic national wildlife refuge’’ [Resour. Energy Econ. 27(4) (2005) 273–286] Jon M. Conrad *, Koji Kotani Cornell University, AEM, 455 Warren Hall, Ithaca, NY, 14853, United States Available online 17 June 2007
Two mistakes were made in calculating the standard deviation rates for the stochastic processes describing oil prices in our paper ‘‘When to Drill? Trigger Prices for the Arctic National Wildlife Refuge,’’ Resource and Energy Economics, 27(4) (2005) 273–286. These mistakes were brought to our attention by Professor Paul Fackler and we are indebted to him for pointing them out. (Professor Fackler has additional comments and concerns about our analysis. See his comment in this volume.) First, we mistakenly used the value of the variance instead of the standard deviation when calculating the trigger prices in the model with geometric Brownian motion (GBM). The correct value in this model should be s = 0.23. Second, we used an incorrect formula in calculating the standard deviation for the mean-reverting (M-R) process. The correct formula and value should be vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ˆ u 2 lnð1 þ bÞ 2ˆh sˆ ¼ sˆ e ¼ 6:3 ¼ sˆ e t ˆ 2 2 h ð1 e Þ ˆ 1 ½ð1 þ bÞ An increase in the standard deviation rate in either model will increase the trigger prices. This effect is quantitatively more pronounced in the GBM model. The corrected trigger prices for our base-case parameter set are given in the table below.
DOI of original article: 10.1016/j.reseneeco.2005.01.001. * Corresponding author. Tel.: +1 607 255 7681; fax: +1 607 255 9984. E-mail address: [email protected] (J.M. Conrad). 0928-7655/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.reseneeco.2007.06.002
Erratum / Resource and Energy Economics 29 (2007) 244–245
245
A (106)
P* GBM (g = h = 0, s = 0.23)
P* M-R (s = 6.3)
$ $ $ $ $ $ $ $ $ $ $
$ $ $ $ $ $ $ $ $ $ $
$ $ $ $ $ $ $ $ $ $ $
200 210 220 230 240 250 260 270 280 290 300
27.96 28.16 28.36 28.56 28.76 28.96 29.16 29.36 29.56 29.76 29.96
27.99 28.61 29.24 29.86 30.49 31.13 31.77 32.42 33.08 33.74 34.41
The corrected trigger prices now range from $ 27.96/bbl to $ 34.41/bbl. In the original paper, with the incorrect standard deviation rates, they ranged from $ 19.84/bbl to $ 31.42/bbl. Oil prices in mid-December, 2005, have ranged between $ 55/bbl and $ 60.00/bbl and would seem to justify exploration and development based on the corrected calibration of our current models.