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Non-Negativity of Nominal and Real Riskless Rates, Arbitrage Theory, and the Null-Alternative Cash

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  • Wilhelm, Jochen
  • Nietert, Bernhard

Abstract

Pragmatic-world nominal riskless rates are non-negative. However, conventional arbitrage theory has yet to develop a theoretical justification of this phenomenon. – We define the null-alternative cash as an investor holding onto cash and refraining from investment and consumption ("doing nothing"); we use the null-alternative cash to prove that both nominal spot and nominal forward rates are non-negative and that prices of zero-coupon bonds do not increase with increasing maturity. In a positive inflation environment, however, both real spot and real forward rates might well become negative, but prices of zero-coupon bonds still do not increase with increasing maturity.

Suggested Citation

  • Wilhelm, Jochen & Nietert, Bernhard, 2004. "Non-Negativity of Nominal and Real Riskless Rates, Arbitrage Theory, and the Null-Alternative Cash," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 11, University of Passau, Faculty of Business and Economics.
    • Handle: RePEc:zbw:upadbr:11
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    References listed on IDEAS

    as
    1. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    2. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
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    Cited by:

    1. Alaeddine Faleh & Fr'ed'eric Planchet & Didier Rulli`ere, 2009. "Les G\'en\'erateurs de Sc\'enarios \'Economiques : quelle utilisation en assurance?," Papers 0911.3472, arXiv.org.
    2. Jochen Wilhelm & Josef Schosser, 2007. "A note on arbitrage-free asset prices with and without personal income taxes," Review of Managerial Science, Springer, vol. 1(2), pages 133-149, August.
    3. Alaeddine Faleh & Frédéric Planchet & Didier Rullière, 2010. "Les générateurs de Scénarios Économiques : de la conception à la mesure de la qualité," Post-Print hal-00530868, HAL.
    4. Alaeddine Faleh & Frédéric Planchet & Didier Rullière, 2010. "Les Générateurs de Scénarios Économiques : quelle utilisation en assurance ?," Post-Print hal-00433037, HAL.

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    More about this item

    Keywords

    arbitrage theory; inflation; non-negativity of spot and forward rates; short selling constraints;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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