scholarly journals A Continuous-Time Model of the Term Structure of Interest Rates with Fiscal-Monetary Policy Interactions

2008 ◽  
Author(s):  
Massimiliano Marzo ◽  
Silvia Romagnoli ◽  
Paolo Zagaglia
Keyword(s):  
Monetary Policy ◽  
Interest Rates ◽  
Term Structure ◽  
Continuous Time ◽  
Continuous Time Model ◽  
Time Model ◽  
Policy Interactions

Discretization of deflated bond prices

2000 ◽  
Vol 32 (2) ◽  
pp. 540-563 ◽  
Author(s):  
Paul Glasserman ◽  
Hui Wang
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Discrete Time ◽  
Continuous Time ◽  
Unit Interval ◽  
Continuous Time Model ◽  
Time Model ◽  
Numerical Work ◽  
Continuous Time Process ◽  
Continuous Time Processes

This paper proposes and analyzes discrete-time approximations to a class of diffusions, with an emphasis on preserving certain important features of the continuous-time processes in the approximations. We start with multivariate diffusions having three features in particular: they are martingales, each of their components evolves within the unit interval, and the components are almost surely ordered. In the models of the term structure of interest rates that motivate our investigation, these properties have the important implications that the model is arbitrage-free and that interest rates remain positive. In practice, numerical work with such models often requires Monte Carlo simulation and thus entails replacing the original continuous-time model with a discrete-time approximation. It is desirable that the approximating processes preserve the three features of the original model just noted, though standard discretization methods do not. We introduce new discretizations based on first applying nonlinear transformations from the unit interval to the real line (in particular, the inverse normal and inverse logit), then using an Euler discretization, and finally applying a small adjustment to the drift in the Euler scheme. We verify that these methods enforce important features in the discretization with no loss in the order of convergence (weak or strong). Numerical results suggest that these methods can also yield a better approximation to the law of the continuous-time process than does a more standard discretization.

Discretization of deflated bond prices

2000 ◽  
Vol 32 (02) ◽  
pp. 540-563 ◽  
Author(s):  
Paul Glasserman ◽  
Hui Wang
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Discrete Time ◽  
Continuous Time ◽  
Unit Interval ◽  
Continuous Time Model ◽  
Time Model ◽  
Numerical Work ◽  
Continuous Time Process ◽  
Continuous Time Processes

This paper proposes and analyzes discrete-time approximations to a class of diffusions, with an emphasis on preserving certain important features of the continuous-time processes in the approximations. We start with multivariate diffusions having three features in particular: they are martingales, each of their components evolves within the unit interval, and the components are almost surely ordered. In the models of the term structure of interest rates that motivate our investigation, these properties have the important implications that the model is arbitrage-free and that interest rates remain positive. In practice, numerical work with such models often requires Monte Carlo simulation and thus entails replacing the original continuous-time model with a discrete-time approximation. It is desirable that the approximating processes preserve the three features of the original model just noted, though standard discretization methods do not. We introduce new discretizations based on first applying nonlinear transformations from the unit interval to the real line (in particular, the inverse normal and inverse logit), then using an Euler discretization, and finally applying a small adjustment to the drift in the Euler scheme. We verify that these methods enforce important features in the discretization with no loss in the order of convergence (weak or strong). Numerical results suggest that these methods can also yield a better approximation to the law of the continuous-time process than does a more standard discretization.

Central Bank Liquidity Management and the Signal Extraction Problem on the Money Market / Die Liquiditätssteuerung der Notenbank und das Signal-extraktionsproblem am Geldmarkt

2000 ◽  
Vol 220 (3) ◽  
pp. 284-301
Author(s):  
Ulrich Bindseil
Keyword(s):  
Monetary Policy ◽  
Central Bank ◽  
Interest Rates ◽  
Term Structure ◽  
Management Strategies ◽  
Money Market ◽  
Signal Extraction ◽  
Maintenance Period ◽  
Liquidity Management ◽  
Expectation Theory

Summary Understanding the factors determining overnight rates is crucial both for central bankers and private market participants, since, assuming the validity of the expectation theory of the term structure of interest rates, expectations with regard to this “monadic” maturity should determine longer term rates, which are deemed to be relevant for the transmission of monetary policy. The note proposes a simple model of the money market within a two-day long reserve maintenance period to derive relationships between the relevant quantities, expectations concerning these quantities for the rest of the reserve maintenance period, and overnight rates. It is argued that a signal extraction problem faced by banks when observing quantities such as their aggregate reserve holdings and allotment amounts of monetary policy operations is at the core of these relationships. The usefulness of the model is illustrated by applying it to the analysis of three alternative liquidity management strategies of a central bank.

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