Interest Rate Volatility and No-Arbitrage Term Structure Models

2012 ◽  
Author(s):  
Scott Joslin ◽  
Anh Le
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Interest Rate Volatility

Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

2021 ◽  
Author(s):  
Scott Joslin ◽  
Anh Le
Keyword(s):  
Term Structure ◽  
Affine Term Structure ◽  
No Arbitrage ◽  
Affine Term Structure Models ◽  
Term Structure Models ◽  
Second Moments ◽  
Interest Rate Volatility ◽  
Rich Information ◽  
The Rich ◽  
Absence Of Arbitrage

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

scholarly journals No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments

2020 ◽  
Vol 17 (1) ◽  
pp. 197-212
Author(s):  
Andrea Tarelli
Keyword(s):  
Interest Rate ◽  
Lower Bound ◽  
Term Structure ◽  
Yield Curve ◽  
Interest Rate Risk ◽  
Information Criteria ◽  
Time Varying ◽  
Term Structure Model ◽  
No Arbitrage ◽  
Term Structure Models

One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

Yield Curves, Swap Curves, and Term Structure of Interest Rates

2019 ◽  
pp. 203-228
Author(s):  
Tom P. Davis ◽  
Dmitri Mossessian
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Yield Curves ◽  
No Arbitrage ◽  
Interest Rate Swap ◽  
The Interest Rate ◽  
Rate Swap ◽  
The U.S

This chapter discusses multiple definitions of the yield curve and provides a conceptual understanding on the construction of yield curves for several markets. It reviews several definitions of the yield curve and examines the basic principles of the arbitrage-free pricing as they apply to yield curve construction. The chapter also reviews cases in which the no-arbitrage assumption is dropped from the yield curve, and then moves to specifics of the arbitrage-free curve construction for bond and swap markets. The concepts of equilibrium and market curves are introduced. The details of construction of both types of the curve are illustrated with examples from the U.S. Treasury market and the U.S. interest rate swap market. The chapter concludes by examining the major changes to the swap curve construction process caused by the financial crisis of 2007–2008 that made a profound impact on the interest rate swap markets.

Collapse of Detail

1998 ◽  
Vol 01 (02) ◽  
pp. 247-282 ◽  
Author(s):  
Enlin Pan
Keyword(s):  
Interest Rate ◽  
State Space ◽  
Explicit Form ◽  
Term Structure ◽  
Degrees Of Freedom ◽  
Functional Form ◽  
No Arbitrage ◽  
Interest Rate Dynamics ◽  
Forward Prices ◽  
Three Degrees Of Freedom

When bond prices can be described in a state-space framework, the no-arbitrage condition and the positivity of forward prices together impose such a tight restriction that only one functional form for the zero-coupon term structure is possible. The explicit form of the term structure is derived, without any parameters. Thus it is unnecessary and even counter-productive to try to specify the nature of interest rate dynamics. Bond pricing has exactly three degrees of freedom.

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