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Performance of utility-based strategies for hedging basis risk


  • Michael Monoyios


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

    1. Wong, Wing-Keung & Li, Chi-Kwong, 1999. "A note on convex stochastic dominance," Economics Letters, Elsevier, vol. 62(3), pages 293-300, March.
    2. Wing-Keung Wong & Meher Manzur & Boon-Kiat Chew, 2003. "How rewarding is technical analysis? Evidence from Singapore stock market," Applied Financial Economics, Taylor & Francis Journals, pages 543-551.
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    Cited by:

    1. 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(06), pages 1361-1395, December.
    2. 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.
    3. Stefan Ankirchner & Gregor Heyne, 2012. "Cross hedging with stochastic correlation," Finance and Stochastics, Springer, vol. 16(1), pages 17-43, January.
    4. 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.
    5. 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.
    6. Thorsten Rheinländer & Gallus Steiger, 2010. "Utility Indifference Hedging with Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, pages 151-169.
    7. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    8. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," Journal of Risk and Financial Management, MDPI, Open Access Journal, pages 1-20.
    9. Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497,, revised Oct 2013.
    10. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Working Papers hal-01086227, HAL.
    11. 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.
    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. 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.
    14. Kim Weston, 2014. "Stability of Utility Maximization in Nonequivalent Markets," Papers 1410.0915,, revised Jun 2015.
    15. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856,, revised Sep 2015.
    16. repec:eee:insuma:v:75:y:2017:i:c:p:1-15 is not listed on IDEAS
    17. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    18. 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.

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