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Pricing and hedging basis risk under no good deal assumption

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  • L. Carassus
  • E. Temam

Abstract

We consider the problem of explicitly pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. We study several prices and in particular the instantaneous no-good-deal price (see Cochrane and Saa-Requejo in J Polit Econ 108(1):79–119, 2001 ) and the global one. We show numerically that the global no-good-deal price can be significantly higher that the instantaneous one. We then propose several hedging strategies and show numerically that the mean-variance hedging strategy can be efficient. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • L. Carassus & E. Temam, 2014. "Pricing and hedging basis risk under no good deal assumption," Annals of Finance, Springer, vol. 10(1), pages 127-170, February.
    • Handle: RePEc:kap:annfin:v:10:y:2014:i:1:p:127-170
    DOI: 10.1007/s10436-013-0246-1
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    References listed on IDEAS

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    1. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    2. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    3. Erhan Bayraktar & Virginia Young, 2008. "Pricing options in incomplete equity markets via the instantaneous Sharpe ratio," Annals of Finance, Springer, vol. 4(4), pages 399-429, October.
    4. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    5. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370.
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    Cited by:

    1. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.
    2. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.

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    More about this item

    Keywords

    No-good-deal; Basis risk; Mean variance hedging; C61; C63; G11; G13;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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