scholarly journals Rating Migration and Bond Valuation: Ahistorical Interest Rate and Default Probability Term Structures

2017 ◽  
Author(s):  
Brian Barnard
Keyword(s):  
Interest Rate ◽  
Default Probability ◽  
Bond Valuation ◽  
Term Structures ◽  
Probability Term

scholarly journals Rating Migration and Bond Valuation: Towards Ahistorical Rating Migration Matrices and Default Probability Term Structures

2019 ◽  
Vol 5 (1) ◽  
pp. 12
Author(s):  
Brian Barnard
Keyword(s):  
Term Structure ◽  
Cash Flows ◽  
Default Probability ◽  
Reduced Form ◽  
Probability Of Default ◽  
Forward Rates ◽  
Bond Valuation ◽  
Term Structures ◽  
Probability Term ◽  
The Impact

The study examines rating migration, and default probability term structures obtained from rating migration matrices. It expands on the use of rating migration matrices with reduced form bond valuation models, by formally delineating the probability of default according to the likely rating paths of a bond, as implied by the rating migration matrix. Further, two alternatives are also considered. First, the cost of default is stipulated as the recovery of par according to the exit rating upon default. Also, in addition to stating the value of a bond in terms of expected cash flows, when considering the probability of default, the value of a bond is alternatively stated as the present value of all likely rating paths of the bond, discounted against the market risk-bearing bond forward rates of the different rating categories. The impact of term structure volatility and rating migration uncertainty on bond valuation is also considered.It is shown that the relationship between rating migration and default probability is complex, and the default probabilities of different rating categories are time-dependent and not isolated from each other. Also, rating migration resembles a delayed default process that influences default probabilities of subsequent intervals. The implications of a rating migration matrix may perhaps only be fully understood through simulation. This form one of the first points by which to evaluate rating migration matrices. The results of the valuation model show that historical rating migration matrices may not be optimal for pricing bonds ahistorically. A principal premise of the study is the dichotomy between historical values and ahistorical estimates, particularly with regards to rating migration. It is argued that historical estimates face two key shortcomings: they must be able to accurately forecast future rating migration and rating category intensities as a result, and they must specify a method to include rating migration uncertainty. An optimization model is delineated to extract ahistorical rating migration matrices from market prices. This too has implications that should be considered. In light of the above, reduced form models may have an advantage over structural models, in their ability to portray a far more sophisticated default process.

Informational Content in Interest Rate Term Structures

1993 ◽  
Vol 75 (4) ◽  
pp. 695 ◽  
Author(s):  
Robert O. Edmister ◽  
Dilip B. Madan
Keyword(s):  
Interest Rate ◽  
Informational Content ◽  
Term Structures

Valuing and Analyzing Bonds with Embedded Options

2019 ◽  
pp. 453-476
Author(s):  
Yiying Cheng
Keyword(s):  
Interest Rate ◽  
Interest Rate Risk ◽  
Convertible Bond ◽  
Callable Bonds ◽  
Bond Valuation ◽  
Specific Risk ◽  
Interest Rate Model ◽  
Embedded Options ◽  
The Difference ◽  
Bond Risk

This chapter introduces the analysis and valuation of bonds with embedded options. For callable bonds, it discusses their unique reinvestment risk and negative convexity. For both callable bonds and puttable bonds, the chapter introduces two additional measures to gauge their risk: yield-to-call and yield-to-put, respectively. The chapter reviews the application of the spot rate curve in bond valuation and introduces the Z-spread to measure bond-specific risk more accurately. To model interest rate risk, the chapter builds a binomial interest rate model and calibrates it with on-the-run Treasury issues. The option-adjusted-spread (OAS) is introduced to measure the bond-specific risk excluding the option effect. The difference between Z-spread and OAS represents the option effect. Common measures of convertible bond risk and value are discussed including the possibility of valuating a convertible bond using option-pricing models and its drawbacks.

scholarly journals Estimating the Short Rate from the Term Structures in the Vasicek Model

2014 ◽  
Vol 61 (1) ◽  
pp. 87-103
Author(s):  
Jana Halgašová ◽  
Beáta Stehlíková ◽  
Zuzana Bučková
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Calibration Method ◽  
Current Level ◽  
Model Parameters ◽  
Bond Prices ◽  
Vasicek Model ◽  
Term Structures ◽  
Short Rate Models

Abstract In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model

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