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Pricing and Hedging Basis Risk under No Good Deal Assumption

  • Laurence Carassus

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris Diderot - Paris 7)

  • Emmanuel Temam

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris Diderot - Paris 7)

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    We consider the problem of 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. Here, following J.H. Cochrane and J. Saá-Requejo, we study valuation under No Good Deal (NGD) Assumption. First, we clarify the notion of NGD for dynamic strategies, compute a lower and an upper bound and prove that in fact NGD price can be strictly higher that the one previously compute in the literature. We also propose a hedging strategy by imposing criterium on the variance of the replication's error. Finally, we provide various numerical illustrations showing the efficiency of NGD pricing and hedging.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/60/94/97/PDF/Good_deal.pdf
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    Paper provided by HAL in its series Working Papers with number hal-00498479.

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    Date of creation: 07 Jul 2010
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    Handle: RePEc:hal:wpaper:hal-00498479
    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00498479/en/
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    1. Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    2. 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.
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