Further evidence on alternative continuous time models of the short-term interest rate

Episcopos, Athanasios

doi:10.1016/s1042-4431(99)00032-3

Cited by 26 publications

(19 citation statements)

References 27 publications

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“…CKLS used the generalised method of moments whilst Nowman (1997Nowman ( , 1998Nowman ( , 2001Nowman ( , 2003 applied Gaussian estimation techniques and Babbs and Nowman (1999) used Kalman filtering methods. Using Gaussian estimation techniques, Episcopos (2000) estimated the parameters of the CKLS type specification for a number of markets. He obtained estimates of the spot rate elasticity of the diffusion term much lower than that obtained by CKLS.…”

Section: Introductionmentioning

confidence: 99%

The volatility of the instantaneous spot interest rate implied by arbitrage pricing—A dynamic Bayesian approach

Bhar¹,

Chiarella²,

Hung³

et al. 2006

Automatica

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This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk-neutral measure and propose a filtering estimation algorithm for a time-discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating in order to estimate the volatility function. Our time discretisation can be justified by the fact that data are observed discretely in time. The method is applied to US Treasury rates of various maturities to compute a (posterior) distribution for the parameters of the volatility specification.

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Section: Introductionmentioning

confidence: 99%

The volatility of the instantaneous spot interest rate implied by arbitrage pricing—A dynamic Bayesian approach

Bhar¹,

Chiarella²,

Hung³

et al. 2006

Automatica

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show abstract

“…However, the short rate, defined as the beginning of the term structure of interest rates, is only a theoretical variable, not observed on the market. In practice, it can be approximated by a yield with short maturity, such as overnight in [5], [6], [8] or 1-month yields in [2], [3], etc. Using 1-month (or some other) yields is, however, not consistent with the interpretation of the short rate as limit of the yields, as maturity approaches zero.…”

Section: P (T T ) = E −R(tt )(T −T) Ie R(t T ) = − Ln P (T Tmentioning

confidence: 99%

“…Using 1-month (or some other) yields is, however, not consistent with the interpretation of the short rate as limit of the yields, as maturity approaches zero. Note that in the papers [2], [3] this problem did not arise, since they considered only one time serie as an approximation of the short rate, not the whole term structure. In [5], [6], [8], when dealing with term structures, overnight was taken to approximate the short rate.…”

Section: P (T T ) = E −R(tt )(T −T) Ie R(t T ) = − Ln P (T Tmentioning

confidence: 99%

Estimating the Short Rate from the Term Structures in the Vasicek Model

Halgašová

Stehlíková

Bučková

2014

Tatra Mountains Mathematical Publications

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ABSTRACT. In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model.

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“…The simple theoretical setting combined with the formalization highlights defining features of the two products and enables a straightforward analysis of the theoretical relations between the two products. There exists a vast body of literature on interest rate models, but there is no consensus on a term structure model that sufficiently captures the real interest rate dynamics while remaining mathematically tractable (e.g., [3,4] and the references therein). The class of (conservative) ATSs primarily fulfil the latter, at the cost of realism.…”

Section: Introductionmentioning

confidence: 99%

What Should You Pay to Cap your ARM?—A Note on Capped Adjustable Rate Mortgages

Nordfang

2017

IJFS

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Abstract:In this paper, an Adjustable Rate Mortgage (ARM) and a Fixed Rate Mortgage (FRM) are formalized and studied in a simple continuous-time setting under the assumption of a simple one-factor Affine Term Structure (ATS). Through an application of existing results from ATS theory, it is shown that when the short rate reaches a certain pre-determined boundary, the constant payment stream on a new FRM equals the payments on an existing ARM. Hereby, this paper provides a theoretical build-in cap on the formalized ARM. The finite boundary for the short-rate suggests that certain caps on ARMs should (in theory) be offered free of charge.

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Further evidence on alternative continuous time models of the short-term interest rate

Cited by 26 publications

References 27 publications

The volatility of the instantaneous spot interest rate implied by arbitrage pricing—A dynamic Bayesian approach

The volatility of the instantaneous spot interest rate implied by arbitrage pricing—A dynamic Bayesian approach

Estimating the Short Rate from the Term Structures in the Vasicek Model

What Should You Pay to Cap your ARM?—A Note on Capped Adjustable Rate Mortgages

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