A general proof of the Dybvig-Ingersoll-Ross theorem: long forward rates can never fall

Hubalek, Friedrich; Klein, Irene; Teichmann, Josef

doi:10.1111/1467-9965.12409

Cited by 20 publications

(33 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the stochastic discount factor M t,τ for period (t, t + τ ) is a positive I t+τ -measurable variable, and E t denotes the conditional expectation given information I t . In particular, we get (see, e.g., Hubalek, Klein, and Teichmann 2002, for an interpretation of the following condition in terms of martingale):…”

Section: The Basic Resultsmentioning

confidence: 99%

Domain Restrictions on Interest Rates Implied by No Arbitrage

Gouriéroux

Monfort

2010

Mathematical Finance

View full text Add to dashboard Cite

show abstract

Section: The Basic Resultsmentioning

confidence: 99%

Domain Restrictions on Interest Rates Implied by No Arbitrage

Gouriéroux

Monfort

2010

Mathematical Finance

View full text Add to dashboard Cite

show abstract

“…(This is consistent with a result of Dybvig, Ingersoll, and Ross 1994, who established that, under the assumption of no arbitrage, a model for the term-structure of interest rates must have a nondecreasing long-term spot rate. For a more rigorous proof of this result, see Hubalek, Klein, and Teichmann 2002. ) The par yield on irredeemable bonds (assuming continuous payment of coupons) is…”

Section: Forward Rates and Irredeemable Bond Yieldsmentioning

confidence: 88%

A Family of Term‐structure Models for Long‐term Risk Management and Derivative Pricing

Cairns¹

2004

Mathematical Finance

View full text Add to dashboard Cite

In this paper we propose a new family of term-structure models based upon the Flesaker & Hughston (1996) positive-interest framework. We demonstrate that the models are ideally suited for use in long-term risk management as well as for shortterm derivative-pricing problems. In particular, the models can be parametrised in a way which gives sustained periods of both high and low interest rates, similar to the cycle lengths we have observed over the course of the 20th century in the UK and US.

show abstract

“…If we recall expression (16) for the pricing kernel in the Vasicek model, and expression (31) for the asymptotic rate, we deduce that the product of the pricing kernel and the long-bond return is given by…”

Section: Long-bond Return Processmentioning

confidence: 99%

Lévy–vasicek Models and the Long-Bond Return Process

Brody

Hughston

Meier

2018

Int. J. Theor. Appl. Finan.

View full text Add to dashboard Cite

The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy-Vasicek case, avoiding issues of market incompleteness. In the Lévy-Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy-Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by L t = lim T →∞ P tT /P 0T , where P tT is the price at time t of a T -maturity discount bond. We show that the pricing kernel of a Lévy-Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

show abstract

A general proof of the Dybvig-Ingersoll-Ross theorem: long forward rates can never fall

Abstract: Abstract. A general proof of the Dybvig-Ingersoll-Ross Theorem on the monotonicity of long forward rates is presented. Some inconsistencies in the original proof of this theorem are discussed.

Cited by 20 publications

References 3 publications

Domain Restrictions on Interest Rates Implied by No Arbitrage

Domain Restrictions on Interest Rates Implied by No Arbitrage

A Family of Term‐structure Models for Long‐term Risk Management and Derivative Pricing

Lévy–vasicek Models and the Long-Bond Return Process

Contact Info

Product

Resources

About