On the Dybvig-Ingersoll-Ross Theorem

Details On the Dybvig-Ingersoll-Ross Theorem On the Dybvig-Ingersoll-Ross Theorem

2009-01-14

arxiv.org/abs/0901.2080v2

Economy

Quantitative Finance

Pricing of Securities

12 pages; second revised version, text rearranged and some content added.

Scientific paper

The Dybvig-Ingersoll-Ross (DIR) theorem states that, in arbitrage-free term structure models, long-term yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that long-term rates at earlier dates can dominate long-term rates at later dates. The viability assumption imposed on the market model is weaker than those appearing previously in the literature.

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