# Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed

@inproceedings{Grant1999ImplementingNT, title={Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed}, author={Dwight Grant and Gautam Vora}, year={1999} }

The article develops a method for implementing nonarbitrage term structure of interest rate models for the single-factor model under the Heath-Jarrow-Morton (HJM) framework of the evolution of forward interest rates. The HJM framework is universal in the sense that it is based on the no-arbitrage condition, and it can accommodate nearly all existing models if interest rates - spot rate and forward rates - distributed normally. The implementation requires the calculation of drift adjustment… Expand

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#### References

SHOWING 1-10 OF 14 REFERENCES

Pricing Interest-Rate-Derivative Securities

- Economics
- 1990

This article shows that the one-state-variable interest-rate models of Vasicek (1977) and Cox, Ingersoll, and Ross (1985b) can be extended so that they are consistent with both the current term… Expand

Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation

- Economics
- 1990

This paper studies the binomial approximation to the continuous trading term structure model of Heath, Jarrow, and Morton (1987). The discrete time approximation makes the original methodology… Expand

Bond pricing and the term structure of interest rates

- Economics
- 1989

This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes… Expand

IMMUNIZATION UNDER STOCHASTIC MODELS OF THE TERM STRUCTURE

- Mathematics, Computer Science
- 1978

The present paper examines the concept of immunization within the framework of these models, it will be shown that Redington's basic idea is still valid although there are important differences within theframework of the stochastic model of the term structure. Expand

Term Structure Movements and Pricing Interest Rate Contingent Claims

- Economics
- 1986

This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term… Expand

Modelling Fixed Income Securities and Interest Rate Options

- Computer Science
- 1995

This book teaches the basics of fixed-income securities in a way that, unlike competitive texts, requires a minimum of prerequisites. While other books focus heavily on institutional details of the… Expand

Stochastic Differential Equations

- Mathematics
- 1998

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion… Expand

An Introduction to the Theory of Statistics

- Mathematics
- Nature
- 1911

OF all the works a man may set himself to write, the most difficult must surely be an elementary text-book on statistics. The writer of a text-book on almost any scientific subject has to face the… Expand

Derivative Securities

- 1996