×

zbMATH — the first resource for mathematics

The stochastic volatility model of Barndorff-Nielsen and shephard in commodity markets. (English) Zbl 1247.91178
The paper investigates the non-Gaussian stochastic volatility model of Barndorff-Nielsen and Shephard for the exponential mean-reversion model of Schwartz proposed for commodity spot prices. It is shown that the log-spot prices possess a stationary distribution defined as a normal variance-mixture model. The model is illustrated for UK gas spot prices. The proposed model is compared to the Heston stochastic volatility model. Explicit forward prices are derived. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91G70 Statistical methods; risk measures
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ait-Sahalia, Testing for Jumps in Disceretely Observed Processes, Ann. Stat. 37 (1) pp 184– (2009)
[2] Barndorff-Nielsen, Processes of Normal Inverse Gaussian Type, Finance Stoch. 2 (1) pp 41– (1998) · Zbl 0894.90011
[3] Barndorff-Nielsen, Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Economics, J. R. Statist. Soc. B 63 (2) pp 167– (2001) · Zbl 0983.60028
[4] Benth, The Normal Inverse Gaussian Distribution and Spot Price Modelling in Energy Markets, Intern. J. Theor. Appl. Finance 7 (2) pp 177– (2004) · Zbl 1107.91309
[5] Benth, Stochastic Modeling of Electricity and Related Markets (2008)
[6] Benth , F. E. L. Vos 2009 A Non-Gaussian Stochastic Volatility Model with Leverage for Commodity Markets http://ssrn.com/abstract=1495156
[7] Börger, A Multivariate Commodity Analysis and Applications to Risk Management, J. Futures Markets 29 (3) pp 197– (2009)
[8] Carr, The Fine Structure of Asset Returns: An Empirical Investigation, J. Business 75 (2) pp 61– (2002) · doi:10.1086/338705
[9] Carr, Option Valuation Using the Fast Fourier Transform, J. Comp. Finance 2 pp 61– (1998) · doi:10.21314/JCF.1999.043
[10] Cox, A Theory of the Term Structure of Interest Rates, Econometrica 53 pp 385– (1981)
[11] Eberlein, Both Sides of a Fence: A Statistical and Regulatory View of Electricity Risk, Energy Risk 8 pp 371– (2003)
[12] Eydeland, Pricing Power Derivatives, RISK (1998)
[13] Geman, Commodities and Commodity Derivatives (2005)
[14] Härdle , W. B. Lopez Cabrera 2009 Discussion Paper
[15] Heston, A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Rev. Finan. Stud. 6 (2) pp 327– (1993) · Zbl 1384.35131
[16] Hikspoors, Asymptotic Pricing of Commodity Derivatives for Stochastic Volatility Spot Models, Appl. Math. Finance 15 (5-6) pp 449– (2007) · Zbl 1156.91374 · doi:10.1080/13504860802170432
[17] Ikeda, Stochastic Differential Equations and Diffusion Processes (1981)
[18] Kallsen, Characterization of Dependence of Multivariate Lévy Processes Using Lévy Copulas, J. Multivar. Anal. 97 (7) pp 1551– (2006)
[19] Karatzas, Brownian Motion and Stochastic Calculus (1991)
[20] Lucia, Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange, Rev. Derivat. Res. 5 (1) pp 5– (2002) · Zbl 1064.91508
[21] Nicolato, Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck Type, Math. Finance 13 (4) pp 445– (2003) · Zbl 1105.91020
[22] Protter, Stochastic Integration and Differential Equations (1990) · doi:10.1007/978-3-662-02619-9
[23] Sato, Lévy Processes and Infinite Divisibility (1999)
[24] Schwartz, The Stochastic Behaviour of Commodity Prices: Implications for Valuation and Hedging, J. Finance LII (3) pp 923– (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.