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Performance of utility-based strategies for hedging basis risk

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  • Michael Monoyios
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    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.

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    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/4/3/001
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 4 (2004)
    Issue (Month): 3 ()
    Pages: 245-255

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    Handle: RePEc:taf:quantf:v:4:y:2004:i:3:p:245-255

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    Cited by:
    1. Thorsten Rheinländer & Gallus Steiger, 2010. "Utility Indifference Hedging with Exponential Additive Processes," Asia-Pacific Financial Markets, Springer, vol. 17(2), pages 151-169, June.
    2. 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.
    3. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    4. 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.
    5. Stefan Ankirchner & Gregor Heyne, 2012. "Cross hedging with stochastic correlation," Finance and Stochastics, Springer, vol. 16(1), pages 17-43, January.
    6. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Feb 2012.
    7. Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497, arXiv.org, revised Oct 2013.
    8. 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.
    9. 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.
    10. Hardy Hulley & T. A. McWalter, 2008. "Quadratic Hedging of Basis Risk," Research Paper Series 225, Quantitative Finance Research Centre, University of Technology, Sydney.

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