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2023 | OriginalPaper | Chapter

13. Spread Options and Virtual Storage

Author : Ilia Bouchouev

Published in: Virtual Barrels

Publisher: Springer Nature Switzerland

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Abstract

We present a trading strategy based on the idea of virtual storage. The physical storage asset is replicated with a financial derivative, a calendar spread option, and the structural pricing dislocation between the physical and financial market is exploited. Other spread option and correlation strategies are based on the concept of a triangular arbitrage, which links prices of vanilla and spread options. We emphasize some flaws of correlation-based models and argue for a closer connection to fundamentals in modeling volatility of energy spreads.

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Footnotes
1
The story of how the strategy was originated and developed is described in Johnson (2022).
 
2
In this chapter, we ignore blending optionality of the storage asset, which allows the owner to mix different grades of crude oil and to sell the blend at a premium by customizing it to the rigorous specifications of a refinery.
 
3
Likewise, the cost of freight determines the strike price of the locational spread option on the difference between oil prices in two different regions. Considine et al. (2022) relates the value of such an option to inventories.
 
4
Formally, this connection follows from reduced-form mean-reverting models, the reference to which are provided in Chap. 3. Less formally and more intuitively, one can see that faster mean-reversion precludes the spread from deviating too far from its mean, which generally results in volatility that declines with time to maturity.
 
5
For more background on spread options that arise in natural gas and power markets, see, for example, Eydeland and Wolyniec (2003) and Swindle (2014).
 
6
Margrabe (1978) derived two-dimensional partial differential equation for the price of a spread option and solved it for K = 0. Kirk (1995) proposed the extension for K ≠ 0 but did not publish its derivation. This formula can be formally derived by applying the method of perturbation introduced in Appendix C. The technical details, however, are rather cumbersome, and given the limited usage of correlation-based pricing formulas in the oil market, we chose not to present them.
 
7
Similar to (A.​10), the solution to the partial differential equation for the price of a spread option can be represented as a double integral of the option payoff multiplied by the risk neutral joint probability density for F1 and F2. Advanced methods for pricing spread options in two-dimensional lognormal setting tend to focus on developing efficient integration techniques and more advanced analytic approximations. See, for example, Shimko (1994), Dempster and Hong (2002), Carmona and Durrleman (2003), and Venkatramanan and Alexander (2011). For petroleum markets, a simple approximation (13.8) is generally sufficient.
 
8
The day when oil prices went negative is removed as neither percentage returns nor standard correlation metrics can even be computed.
 
9
Technically, the volatility of the first leg is also not observable as a vanilla option expires three days prior to futures but the corresponding CSO expires one day before futures. Traders often make an additional ad hoc adjustment to the implied volatility of a vanilla option to incorporate this effect.
 
Literature
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go back to reference Dempster, M. A. H., & Hong, S. S. G. (2002). Spread option valuation and the fast Fourier transform. In H. Geman, D. Madan, S. R. Pliska, & T. Vorst (Eds.), Mathematical finance, Bachelier congress (Vol. 1, pp. 203–220). Springer.CrossRef Dempster, M. A. H., & Hong, S. S. G. (2002). Spread option valuation and the fast Fourier transform. In H. Geman, D. Madan, S. R. Pliska, & T. Vorst (Eds.), Mathematical finance, Bachelier congress (Vol. 1, pp. 203–220). Springer.CrossRef
go back to reference Eydeland, A., & Wolyniec, K. (2003). Energy and power risk management: New developments in modeling, pricing, and hedging. Wiley. Eydeland, A., & Wolyniec, K. (2003). Energy and power risk management: New developments in modeling, pricing, and hedging. Wiley.
go back to reference Johnson, O. (2022). 40 classic crude oil trades: Real-life examples of innovative trading. Routledge. Johnson, O. (2022). 40 classic crude oil trades: Real-life examples of innovative trading. Routledge.
go back to reference Kirk, E. (1995). Correlation in the energy markets. In Managing energy price risk (pp. 71–78). Risk Publications. Kirk, E. (1995). Correlation in the energy markets. In Managing energy price risk (pp. 71–78). Risk Publications.
go back to reference Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33(1), 177–186.CrossRef Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33(1), 177–186.CrossRef
go back to reference Shimko, D. C. (1994). Options on futures spreads: Hedging, speculation, and valuation. The Journal of Futures Markets, 14(2), 183–213.CrossRef Shimko, D. C. (1994). Options on futures spreads: Hedging, speculation, and valuation. The Journal of Futures Markets, 14(2), 183–213.CrossRef
go back to reference Swindle, G. (2014). Valuation and risk management in energy markets. Cambridge University Press.CrossRef Swindle, G. (2014). Valuation and risk management in energy markets. Cambridge University Press.CrossRef
go back to reference Venkatramanan, A., & Alexander, C. (2011). Closed form approximations for spread options. Applied Mathematical Finance, 18(5), 447–472.MathSciNetCrossRefMATH Venkatramanan, A., & Alexander, C. (2011). Closed form approximations for spread options. Applied Mathematical Finance, 18(5), 447–472.MathSciNetCrossRefMATH
Metadata
Title
Spread Options and Virtual Storage
Author
Ilia Bouchouev
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-36151-7_13