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Option Pricing with Differential Interest Rates

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  • Bergman, Yaacov Z
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    Abstract

    The classic option pricing model is generalized to a more realistic, imperfect, dynamically incomplete capital market with different interest rates for borrowing and for lending and a return differential between long and short positions in stock. It is found that, in the absence of arbitrage opportunities, the equilibrium price of any contingent claim must lie within an arbitrage-band. The boundaries of an arbitrage-band are computed as solutions to a quasi-linear partial differential equation, and, in generals each end-point of such a band depends on both interest rates for borrowing and for lending. This, in turn, implies that the vector of concurrent equilibrium prices of different contingent claims - even claims that are written on different underlying assets - must lie within a computable arbitrage-oval in the price space. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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    Bibliographic Info

    Article provided by Society for Financial Studies in its journal Review of Financial Studies.

    Volume (Year): 8 (1995)
    Issue (Month): 2 ()
    Pages: 475-500

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    Handle: RePEc:oup:rfinst:v:8:y:1995:i:2:p:475-500

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    Cited by:
    1. Damiano Brigo & Andrea Pallavicini, 2014. "CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach," Papers 1401.3994, arXiv.org.
    2. Tomasz R. Bielecki & Marek Rutkowski, 2014. "Valuation and Hedging of Contracts with Funding Costs and Collateralization," Papers 1405.4079, arXiv.org, revised Jul 2014.
    3. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    4. Fehle, Frank, 2004. "A note on transaction costs and the existence of derivatives markets," Journal of Economics and Business, Elsevier, vol. 56(1), pages 63-70.
    5. Thilo Moseler & Christian Bender, 2008. "Importance sampling for backward SDEs," CoFE Discussion Paper 08-11, Center of Finance and Econometrics, University of Konstanz.
    6. Mirschel, Stefan, 2006. "Dualitätstheoretische Untersuchung des Einigungsbereichs von Optionsgeschäften auf unvollkommenen Märkten," Wirtschaftswissenschaftliche Diskussionspapiere 08/2006, Ernst Moritz Arndt University of Greifswald, Faculty of Law and Economics.
    7. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
    8. Kallio, Markku & Ziemba, William T., 2007. "Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2281-2302, August.

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