No-Arbitrage Models of the Term Structure: Ho-Lee and Heath-Jarrow-Morton

2011 ◽  
pp. 291-295
Keyword(s):  
Term Structure ◽  
No Arbitrage

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.

scholarly journals GENERAL ANALYSIS OF LONG-TERM INTEREST RATES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050002
Author(s):  
FRANCESCA BIAGINI ◽  
ALESSANDRO GNOATTO ◽  
MAXIMILIAN HÄRTEL
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Applied Mathematics ◽  
Mathematical Finance ◽  
Rational Model ◽  
No Arbitrage ◽  
Working Paper ◽  
Social Discounting ◽  
The Relationship

We introduce here the idea of a long-term swap rate, characterized as the fair rate of an overnight indexed swap (OIS) with infinitely many exchanges. Furthermore, we analyze the relationship between the long-term swap rate, the long-term yield, (F. Biagini, A. Gnoatto & M. Härtel (2018) Affine HJM Framework on [Formula: see text] and long-term yield, Applied Mathematics and Optimization 77 (3), 405–441, F. Biagini & M. Härtel (2014) Behavior of long-term yields in a lévy term structure, International Journal of Theoretical and Applied Finance 17 (3), 1–24, N. El Karoui, A. Frachot & H. Geman (1997) A note on the behavior of long zero coupon rates in a no arbitrage framework. Working Paper. Available at Researchgate: https://www.researchgate.net/publication/5066730) , and the long-term simple rate (D. C. Brody & L. P. Hughston (2016) Social discounting and the long rate of interest, Mathematical Finance 28 (1), 306–334) as long-term discounting rate. Finally, we investigate the existence of these long-term rates in two-term structure methodologies, the Flesaker–Hughston model and the linear-rational model. A numerical example illustrates how our results can be used to estimate the nonoptional component of a CoCo bond.

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.

Estimation of Peru’s sovereign yield curve: the role of macroeconomic and latent factors

2019 ◽  
Vol 46 (3) ◽  
pp. 533-563
Author(s):  
Alejandra Olivares Rios ◽  
Gabriel Rodríguez ◽  
Miguel Ataurima Arellano
Keyword(s):  
Term Structure ◽  
Risk Premium ◽  
Yield Curve ◽  
International Markets ◽  
Bond Yields ◽  
Content Type ◽  
Vector Autoregressive ◽  
Term Structure Model ◽  
No Arbitrage ◽  
Unobservable Factors

PurposeFollowing Ang and Piazzesi’s (2003) study, the authors use an affine term structure model to study the relevance of macroeconomic (domestic and foreign) factors for Peru’s sovereign yield curve in the period from November 2005 to December 2015. The paper aims to discuss this issue.Design/methodology/approachRisk premia are modeled as time-varying and depend on both observable and unobservable factors; and the authors estimate a vector autoregressive model considering no-arbitrage assumptions.FindingsThe authors find evidence that macro factors help to improve the fit of the model and explain a substantial amount of variation in bond yields. However, their influence is very sensitive to the specification model. Variance decompositions show that macro factors explain a significant share of the movements at the short and middle segments of the yield curve (up to 50 percent), while unobservable factors are the main drivers for most of the movements at the long end of the yield curve (up to 80 percent). Furthermore, the authors find that international markets are relevant for the determination of the risk premium in the short term. Higher uncertainty in international markets increases bond yields, although this effect vanishes quickly. Finally, the authors find that no-arbitrage restrictions with the incorporation of macro factors improve forecasts.Originality/valueTo the authors’ knowledge this is the first application of this type of models using data from an emerging country such as Peru.

scholarly journals Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates

2019 ◽  
Vol 33 (8) ◽  
pp. 3719-3765 ◽  
Author(s):  
Andrea Ajello ◽  
Luca Benzoni ◽  
Olena Chyruk
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Real Term ◽  
No Arbitrage ◽  
Market Participants ◽  
Oxford University ◽  
Term Structures ◽  
Consumer Prices ◽  
Real Risk ◽  
Pass Through

Abstract We propose a no-arbitrage model of the nominal and real term structures that accommodates the different persistence and volatility of distinct inflation components. Core, food, and energy inflation combine into a single total inflation measure that ties nominal and real risk-free bond prices together. The model successfully extracts market participants’ expectations of future inflation from nominal yields and inflation data. Estimation uncovers a factor structure common to core inflation and interest rates and downplays the pass-through effect of short-lived food and energy shocks on inflation and interest rates. Model forecasts systematically outperform survey forecasts and other benchmarks. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

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