The Dynamics of Credit Spreads and Ratings Migrations

2007 ◽  
Vol 42 (3) ◽  
pp. 595-620 ◽  
Author(s):  
Heber Farnsworth ◽  
Tao Li
Keyword(s):  
Term Structure ◽  
Bayes Factor ◽  
Historical Data ◽  
Transition Probabilities ◽  
Credit Spreads ◽  
Free Term ◽  
State Variables ◽  
Yield Curves ◽  
Nested Models ◽  
The Bayesian Approach

AbstractThere is a large and growing literature on how to model the dynamics of the default-free term structure to fit the observed historical data. Much less is known about how best to model the dynamics of defaultable yield curves. This paper develops a class of defaultable term structure models that is tractable enough to be empirically implemented and flexible enough to capture some important behaviors of the credit spreads in the data. We compare two non-nested models within this class using a Bayesian estimation technique, which helps to solve the problem of latent state variables. The Bayesian approach also enables us to test the two non-nested models on the basis of the Bayes factor. The results strongly suggest that models with constant transition probabilities will not be able to fit the observed dynamics of inter-rating spreads.

CORRELATION ANALYSIS IN THE LIBOR AND SWAP MARKET MODEL

2002 ◽  
Vol 05 (04) ◽  
pp. 401-426 ◽  
Author(s):  
ETIENNE DE MALHERBE
Keyword(s):  
Probability Measure ◽  
Term Structure ◽  
Joint Distribution ◽  
General Framework ◽  
Historical Data ◽  
Market Model ◽  
Yield Curves ◽  
Drift Term ◽  
Correlation Term ◽  
Swap Rates

In the general framework that is offered by the market model, each LIBOR interest rate is a lognormal martingale under its own probability measure. The advantage is that the approach is consistent with the way cap, floor and swaption volatilities are quoted. The joint distribution of several LIBOR or swap rates under a common probability measure is somehow more complicated because it requires the specification of a drift term structure and the specification of a correlation term structure. In this paper, the correlation between the LIBORs is represented by a function of the LIBOR maturities. The form of this function is inspired by the stochastic string theory that was recently introduced in finance for the modelling of yield curves. The function is fitted to the volatilities of the LIBOR and swap rates so that it is consistent with market observations and does not rely on statistical analysis of any historical data.

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.

BAYESIAN OCKHAM’S RAZOR AND NESTED MODELS

2019 ◽  
Vol 35 (02) ◽  
pp. 321-338
Author(s):  
Bengt Autzen
Keyword(s):  
Bayesian Approach ◽  
Bayesian Methods ◽  
Economic Models ◽  
Philosophical Literature ◽  
Ockham’S Razor ◽  
Nested Models ◽  
Scientific Inference ◽  
Complex Hypothesis ◽  
Ockham's Razor ◽  
The Bayesian Approach

Abstract:While Bayesian methods are widely used in economics and finance, the foundations of this approach remain controversial. In the contemporary statistical literature Bayesian Ockham’s razor refers to the observation that the Bayesian approach to scientific inference will automatically assign greater likelihood to a simpler hypothesis if the data are compatible with both a simpler and a more complex hypothesis. In this paper I will discuss a problem that results when Bayesian Ockham’s razor is applied to nested economic models. I will argue that previous responses to the problem found in the philosophical literature are unsatisfactory and develop a novel reply to the problem.

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