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2023 | OriginalPaper | Buchkapitel

11. Volatility Term Structure and Exotic Options

verfasst von : Ilia Bouchouev

Erschienen in: Virtual Barrels

Verlag: Springer Nature Switzerland

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Abstract

We describe arguably the most significant oil derivative trade, the large-scale annual put buying program by the Government of Mexico. The complexity of over-the-counter deals highlights the importance of handling the volatility term structure and the effect of volatility dampening by price averaging. A simplified and more practical model for pricing and hedging average price options, which are popular among end-users, is presented. Swaptions and other exotic derivatives are also discussed.

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Fußnoten
1
It should be noted that oil exchanges did exist in Pennsylvania and New York as early as in the 1870s, see Giddens (1947). However, all of them were closed within a decade under monopolistic pressure from the Standard Oil Company.
 
2
For a colorful description of the history of this program, see Blas (2017).
 
3
Prior to 2019, the Maya formula was calculated as 40% WTS (West Texas Sour), 40% HSFO (High-Sulfur Fuel Oil), 10% LLS (Louisiana Light Sweet), 10% Dated Brent, plus a K-factor set by Mexico. To reflect the growth in US shale and changes in the sulfur specification for marine fuel, in 2019 the formula changed to 65% WTI Houston, 35% ICE Brent, plus a K-factor.
 
4
Merton (1973).
 
5
There is a large body of literature on pricing APOs. Kemna and Vorst (1990) formulated the partial differential equation for the price of an APO and found a closed-form solution for an option on the geometric average of prices. Such a solution is possible because the geometric average of lognormal variables is also lognormal. Subsequently, many authors used the idea of geometric averages to develop approximations of the probability density function for the arithmetic average of lognormal variables and corresponding approximations for APO prices, such as the formulas of Turnbull and Wakeman (1991) and Levy (1992). For other APO pricing methods, see also Wilmott et al. (1993), Lipton (2001), and Geman (2005). The method described in this book was originally suggested in Bouchouev (2000).
 
6
For non-zero interest rates ri that correspond to times Ti, the swap value S is determined by equating the present value of the future cash flows to zero: \( \sum \limits_{i=1}^M{e}^{-{r}_i\left({T}_i-t\right)}\left(S-{F}_i\right)=0. \) Solving it for S, we obtain that S is given by (11.15) with \( {\omega}_i={e}^{-{r}_i\left({T}_i-t\right)}/\sum \limits_{i=1}^M{e}^{-{r}_i\left({T}_i-t\right)} \).
 
7
For more details on the time-scale separation for pricing natural gas and power options, see Swindle (2014).
 
Literatur
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Zurück zum Zitat Bouchouev, I. (2000, July). Demystifying Asian options. Energy and Power Risk Management, pp. 26–27. Bouchouev, I. (2000, July). Demystifying Asian options. Energy and Power Risk Management, pp. 26–27.
Zurück zum Zitat Geman, H. (2005). Commodities and commodity derivatives: Modeling and pricing for agriculturals, metals and energy. Wiley. Geman, H. (2005). Commodities and commodity derivatives: Modeling and pricing for agriculturals, metals and energy. Wiley.
Zurück zum Zitat Giddens, P. H. (1947). Pennsylvania petroleum 1750–1872: A documentary history. Pennsylvania Historical and Museum Commission. Giddens, P. H. (1947). Pennsylvania petroleum 1750–1872: A documentary history. Pennsylvania Historical and Museum Commission.
Zurück zum Zitat Kemna, A. G. Z., & Vorst, A. C. F. (1990). A pricing method for options based on average asset values. Journal of Banking and Finance, 14(1), 113–129.CrossRef Kemna, A. G. Z., & Vorst, A. C. F. (1990). A pricing method for options based on average asset values. Journal of Banking and Finance, 14(1), 113–129.CrossRef
Zurück zum Zitat Levy, E. (1992). Pricing European average rate currency options. Journal of International Money and Finance, 11(5), 474–491.CrossRef Levy, E. (1992). Pricing European average rate currency options. Journal of International Money and Finance, 11(5), 474–491.CrossRef
Zurück zum Zitat Lipton, A. (2001). Mathematical methods for foreign exchange: A financial engineer’s approach. World Scientific.CrossRefMATH Lipton, A. (2001). Mathematical methods for foreign exchange: A financial engineer’s approach. World Scientific.CrossRefMATH
Zurück zum Zitat Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141–183.MathSciNetCrossRefMATH Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141–183.MathSciNetCrossRefMATH
Zurück zum Zitat 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
Zurück zum Zitat Turnbull, S. M., & Wakeman, L. M. (1991). A quick algorithm for pricing European average price options. Journal of Financial and Quantitative Analysis, 26(3), 377–389.CrossRef Turnbull, S. M., & Wakeman, L. M. (1991). A quick algorithm for pricing European average price options. Journal of Financial and Quantitative Analysis, 26(3), 377–389.CrossRef
Zurück zum Zitat Wilmott, P., Dewynne, J., & Howison, S. (1993). Option pricing: Mathematical models and computation. Oxford Financial Press.MATH Wilmott, P., Dewynne, J., & Howison, S. (1993). Option pricing: Mathematical models and computation. Oxford Financial Press.MATH
Metadaten
Titel
Volatility Term Structure and Exotic Options
verfasst von
Ilia Bouchouev
Copyright-Jahr
2023
DOI
https://doi.org/10.1007/978-3-031-36151-7_11