Top

Mathematics and Financial Economics

Published in:

16-08-2018

Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option

Authors: Indranil SenGupta, William Wilson, William Nganje

Published in: Mathematics and Financial Economics | Issue 2/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The results indicate that oil can be optimally hedged with the use of a combination of options and variance swaps. Theoretical results related to the variance process are established and implemented for the analysis of the variance swap. In this paper we also determined the optimal amount of the underlying oil commodity that has to be held for minimizing the hedging error. The model and analysis are used to numerically analyze hedging decisions for managing price risk in Bakken oil commodities. From the numerical results, a number of important features of the usefulness of the Barndorff-Nielsen and Shephard model are illustrated.

previous article Borrowing constraints, effective flexibility in labor supply, and portfolio selection

next article Turnpike property and convergence rate for an investment and consumption model

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Awudu, I., Wilson, W., Dahl, B.: Hedging strategy for ethanol processing with copula distributions. Energy Econ. 57, 59–65 (2016)CrossRef

Bakx, K.: Alberta Budget 2016: How to find the right price for oil, bull or bear? Alberta’s NDP government must forecast how much in royalties it will collect in next year. CBC News. http://www.cbc.ca/news/canada/calgary/alberta-budget-oil-prices-first-energy-1.3532141 (2016). Accessed 13 Apr 2016

Barndorff-Nielsen, O.E.: Superposition of Ornstein–Uhlenbeck type processes. Theory Probab. Appl. 45, 175–194 (2001)MathSciNetCrossRefMATH

Barndorff-Nielsen, O.E.: Integrated OU processes and non-Gaussian OU-based stochastic volatility models. Scand. J. Stat. 30(2), 277–295 (2003)MathSciNetCrossRefMATH

Barndorff-Nielsen, O.E., Jensen, J.L., Sørensen, M.: Some stationary processes in discrete and continuous time. Adv. Appl. Probab. 30, 989–1007 (1998)MathSciNetCrossRefMATH

Barndorff-Nielsen, O.E., Shephard, N.: Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 63, 167–241 (2001)MathSciNetCrossRefMATH

Barndorff-Nielsen, O.E., Shephard, N.: Modelling by Lévy processes for financial econometrics. In: Barndorff-Nielsen, O.E., Mikosch, T., Resnick, S. (eds.) Lévy Processes: Theory and Applications, pp. 283–318. Birkhäuser, Basel (2001)CrossRef

Barndorff-Nielsen, O.E., Shephard, N.: Basics of Lévy processes, draft chapter from a book by the authors on Lévy Driven Volatility Models. https://pdfs.semanticscholar.org/fe80/07ba98fafa23ddca98ac5d9b1cf1732f70bd.pdf (2012). Accessed 13 Mar 2016

Blas, J., Martin, E.: World’s Largest Oil Hedge Set to Make Billions for Mexican States, Bloomberg: Quint https://www.bloombergquint.com/onweb/2016/08/02/mexico-set-for-2016-windfall-from-sovereign-oil-price-hedge-irej4npe (2016). Accessed 16 Aug 2016

10.

Caruana, J.M.: Should governments hedge oil? Times of Malta. https://www.timesofmalta.com/articles/view/20150215/business-news/Should-governments-hedge-oil-.556199 (2015). Accessed 15 Feb 2015

11.

Cifuentes, E.: Mexico Made \$3 billion from Oil Hedging in 2016-What is their 2017 Strategy? http://oilprice.com/Energy/Energy-General/Mexico-Made-3-Billion-From-Oil-Hedging-In-2016-What-is-Their-2017-Strategy.html (2016). Accessed 7 Aug 2016

12.

Cont, R., Tankov, P.: Financial Modelling with Jump Processes. CRC Financial Mathematics Series. Chapman and Hall, London (2004)MATH

13.

Cont, R., Voltchkova, E.: Integro-differential equations for option prices in exponential Lévy models. Finance Stoch. 9, 299–325 (2005)MathSciNetCrossRefMATH

14.

Daniel, J.: Hedging Government Oil Price Risk, International Monetary Fund. IMF Working Paper, WP/01/185: pp. 1–21. https://www.imf.org/external/pubs/ft/wp/2001/wp01185.pdf (2001). Accessed Nov 2001

15.

Farchy, J.: Russia Considers Hedging Part of its Oil Revenues. Financial Times. https://www.ft.com/content/4b533980-c122-11e5-846f-79b0e3d20eaf (2016). Accessed 22 Jan 2016

16.

Figueroa-López, J.E.: Statistical estimation of Lévy-type stochastic volatility models. Ann. Finance 8, 309–335 (2012)MathSciNetCrossRefMATH

17.

Franck, T.: Gas prices fall after Hurricane Irma destruction not as bad as feared. https://www.cnbc.com/2017/09/11/gas-prices-fall-after-hurricane-irma-destruction-not-as-bad-as-feared.html (2017). Retrieved 11 Sept 2017

18.

Geman, H.: Commodities and commodity derivatives: modeling and pricing for agriculturals, metals and energy, 1st edn. Wiley (2009)

19.

Haavardsrud, P.: Oil price hedging by governments can be a smart bet or a bad gamble. CBC News, posted. http://www.cbc.ca/news/business/hedging-oil-provincial-budgets-1.3530084 (2016). Accessed 13 Apr 2016

20.

Habtemicael, S., SenGupta, I.: Ornstein–Uhlenbeck processes for geophysical data analysis. Phys. A Stat. Mech. Appl. 399, 147–156 (2014)MathSciNetCrossRefMATH

21.

Habtemicael, S., SenGupta, I.: Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets. Int. J. Financ. Eng. 03(04), 1650027 (2016)MathSciNetCrossRef

22.

Habtemicael, S., SenGupta, I.: Pricing covariance swaps for Barndorff-Nielsen and Shephard process driven financial markets. Ann. Financ. Econ. 11, 1650012 (2016)CrossRef

23.

Habtemicael, S., Ghebremichael, M., SenGupta, I.: Volatility and variance swap using superposition of the Barndorff-Nielsen and Shephard type Lévy processes. Sankhya B, accepted in September 2017. https://doi.org/10.1007/s13571-017-0145-y (2018)

24.

Hill, A.: Government Oil Hedge Underwater. The Gleaner. http://jamaica-gleaner.com/article/business/20160115/aubyn-hill-government-oil-hedge-underwater (2016). Accessed 15 Jan 2016

25.

Holz, J., Untershultz, J.U.: Hedging Alberta Government’s Oil and Gas Revenue: Is Acting Like a Farmer a Viable Strategy, Staff Paper #09-01, Department of Rural Economy Faculty of Agricultural, Life and Environmental Sciences, University of Alberta, Edmonton (2009)

26.

Hubalek, F., Posedel, P.: Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models. Quant. Finance 11(6), 917–932 (2011)MathSciNetCrossRefMATH

27.

Hull, J.: Fundamentals of Futures and Options Markets, 5th edn. Pearson Prentice Hall, Boston (2005)MATH

28.

Issaka, A., SenGupta, I.: Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index. Ann. Finance 13(4), 401–434 (2017)MathSciNetCrossRefMATH

29.

James, T.: Energy Markets: Price Risk Management and Trading. Wiley, Hoboken (2007)

30.

Kelly, K.: The Secret Club That Runs the World: Inside the Fraternity of Commodity Traders. Hardcover Penguin Portfolio, New York (2014)

31.

Kolb, R.: The Natural Gas Revolution. Pearson, Upper Saddle River (2013)

32.

Kolb, R., Overdahl, J.: Understanding Futures Markets, 6th edn. Wiley-Blackwell Publishing, Oxford (2006)

33.

Larsson, K., Nossman, M.: Jumps and stochastic volatility in oil prices: time series evidence. Energy Econ. 33, 504–514 (2011)CrossRef

34.

Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)

35.

Matthews, C., Olson, B.: Oil is above \$70, but frackers still struggle to make money. Wall Street J. https://www.wsj.com/articles/oils-at-70-but-frackers-still-struggling-to-make-money-1526549401 (2018). Accessed 17 May 2018

36.

Montes, J.: Mexico Enters \$76.40 Oil Price Hedge for 2015: Program Allowed Country to Avoid Major Budget Crisis When Crude Prices Sank in 2009. Wall Street J. https://www.wsj.com/articles/mexico-enters-76-40-oil-price-hedge-for-2015-1415917558 (2014). Accessed 13 Nov 2014

37.

Nicolato, E., Venardos, E.: Option pricing in stochastic volatility models of the Ornstein–Uhlenbeck type. Math. Finance 13, 445–466 (2003)MathSciNetCrossRefMATH

38.

Percival, G.: Ryanair surges but profits set to fall this year. Irish Examiner. http://aws2.irishexaminer.com/breakingnews/business/ryanair-surges-but-profits-set-to-fall-this-year-844273.html (2018). Accessed 22 May 2018

39.

Price, K.: Hedging is an effective risk management tool for upstream companies, Société Generale, London. http://www.ogfj.com/articles/print/volume-9/issue-11/features/etrm/hedging-is-an-effective-risk-management.html (2012). Accessed 11 Nov 2012

40.

Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)MATH

41.

SenGupta, I.: Option pricing with transaction costs and stochastic interest rate. Appl. Math. Finance 21, 399–416 (2014)MathSciNetCrossRefMATH

42.

SenGupta, I.: Generalized BN-S stochastic volatility model for option pricing. Int. J. Theor. Appl. Finance 19(02), 1650014 (2016)MathSciNetCrossRefMATH

43.

Swidler, S., Butimer, R., Shaw, R.: Government hedging: motivation, implementation and evaluation. Public Budg. Finance 19, 75–90 (2004)CrossRef

44.

Swishchuk, A.: Modeling of variance and volatility swaps for financial markets with stochastic volatilities. Wilmott Magazine, September, Technical article No 2, 64–72 (2004)

45.

Swishchuk, A.: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities. World Scientific Publishing Company, Singapore (2013)CrossRefMATH

46.

The Guardian (2015): Ryanair warns plunging oil price will hurt profits. https://www.theguardian.com/business/2015/feb/02/ryanair-warns-plunging-oil-price-hurt-profits. Accessed 2 Feb 2015

47.

Wolfe, S.J.: On a continuous analogue of the stochastic difference equation $\rho X_{n+1}+B_n$. Stoch. Process. Appl. 12, 301–312 (1982)CrossRef

48.

Yun, W.C., Kim, H.J.: Hedging strategy for crude oil trading and the factors influencing hedging effectiveness. Energy Policy 38(5), 2404–2408 (2010)CrossRef

49.

Zahradnik, R., Iyengar, A., Zhang, A.: Tax Revenue Volatility Poses Budget Challenges for Some States, Pew Charitable Trusts. http://www.pewtrusts.org/en/research-and-analysis/analysis/2017/02/02/tax-revenue-volatility-poses-budget-challenges-for-some-states (2017). Accessed 2 Feb 2017

Title: Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option
Authors: Indranil SenGupta
William Wilson
William Nganje
Publication date: 16-08-2018
Publisher: Springer Berlin Heidelberg
Published in: Mathematics and Financial Economics / Issue 2/2019
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-018-0225-4

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 2/2019

Turnpike property and convergence rate for an investment and consumption model

Characterizations of risk aversion in cumulative prospect theory

Increasing risk aversion and life-cycle investing

Optimal investment with random endowments and transaction costs: duality theory and shadow prices

Borrowing constraints, effective flexibility in labor supply, and portfolio selection