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Performance of utility-based strategies for hedging basis risk

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  • Michael Monoyios

Abstract

The performance of optimal strategies for hedging a claim on a non-traded asset is analysed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation ρ typically close to 1. Using a distortion method (Zariphopoulou 2001 Finance Stochastics 5 61-82) we derive a nonlinear expectation representation for the claim's ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of ε2 =1-ρ2. The terms in the price expansion are proportional to the central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation-based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyse hedging performance. We find that the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies. An empirical example illustrates the application of the method to the hedging of a stock basket using index futures.

Suggested Citation

  • Michael Monoyios, 2004. "Performance of utility-based strategies for hedging basis risk," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 245-255.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:3:p:245-255
    DOI: 10.1088/1469-7688/4/3/001
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    References listed on IDEAS

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    Cited by:

    1. Stefan Ankirchner & Gregor Heyne, 2012. "Cross hedging with stochastic correlation," Finance and Stochastics, Springer, vol. 16(1), pages 17-43, January.
    2. Weidong Tian & Daisuke Yoshikawa, 2017. "Analyzing Equilibrium in Incomplete Markets with Model Uncertainty," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 235-262, June.
    3. Xu, Wei & Odening, Martin & Musshoff, Oliver, 2007. "Indifference Pricing of Weather Insurance," 101st Seminar, July 5-6, 2007, Berlin Germany 9267, European Association of Agricultural Economists.
    4. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    5. Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497, arXiv.org, revised Oct 2013.
    6. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Working Papers hal-01086227, HAL.
    7. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    8. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    9. Ankirchner, Stefan & Dimitroff, Georgi & Heyne, Gregor & Pigorsch, Christian, 2012. "Futures Cross-Hedging with a Stationary Basis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(6), pages 1361-1395, December.
    10. Michael Monoyios, 2010. "Utility-Based Valuation and Hedging of Basis Risk With Partial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 519-551.
    11. Thorsten Rheinländer & Gallus Steiger, 2010. "Utility Indifference Hedging with Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(2), pages 151-169, June.
    12. Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    13. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    14. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.
    15. Giorgia Callegaro & Luciano Campi & Valeria Giusto & Tiziano Vargiolu, 2017. "Utility indifference pricing and hedging for structured contracts in energy markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 265-303, April.
    16. Bauer Jan, 2020. "Hedging of Variable Annuities under Basis Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-34, July.
    17. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
    18. Kim Weston, 2014. "Stability of Utility Maximization in Nonequivalent Markets," Papers 1410.0915, arXiv.org, revised Jun 2015.
    19. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    20. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1606-1620, November.
    21. Laurence Carassus & Massinissa Ferhoune, 2021. "Efficient approximations for utility-based pricing," Papers 2105.08804, arXiv.org, revised Feb 2024.
    22. Ming Pu & Gang-Zhi Fan & Seow Ong, 2012. "Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 44(4), pages 543-569, May.
    23. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.
    24. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Post-Print hal-01086227, HAL.

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