scholarly journals The Two-Parameter Formula of Default Probability Term Structure

2018 ◽  
Vol 23 (4) ◽  
pp. 419-432
Author(s):  
M.V. Pomazanov ◽  
Keyword(s):  
Term Structure ◽  
Default Probability ◽  
Probability Term ◽  
Two Parameter

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.

CDS-based implied probability of default estimation

2020 ◽  
Vol 21 (4) ◽  
pp. 399-422
Author(s):  
Amira Abid ◽  
Fathi Abid ◽  
Bilel Kaffel
Keyword(s):  
Credit Risk ◽  
Term Structure ◽  
Transition Matrix ◽  
Risk Model ◽  
Default Probability ◽  
Probability Of Default ◽  
Content Type ◽  
Thomson Reuters ◽  
Investment Grade ◽  
Implied Default Probability

Purpose This study aims to shed more light on the relationship between probability of default, investment horizons and rating classes to make decision-making processes more efficient. Design/methodology/approach Based on credit default swaps (CDS) spreads, a methodology is implemented to determine the implied default probability and the implied rating, and then to estimate the term structure of the market-implied default probability and the transition matrix of implied rating. The term structure estimation in discrete time is conducted with the Nelson and Siegel model and in continuous time with the Vasicek model. The assessment of the transition matrix is performed using the homogeneous Markov model. Findings The results show that the CDS-based implied ratings are lower than those based on Thomson Reuters approach, which can partially be explained by the fact that the real-world probabilities are smaller than those founded on a risk-neutral framework. Moreover, investment and sub-investment grade companies exhibit different risk profiles with respect of the investment horizons. Originality/value The originality of this study consists in determining the implied rating based on CDS spreads and to detect the difference between implied market rating and the Thomson Reuters StarMine rating. The results can be used to analyze credit risk assessments and examine issues related to the Thomson Reuters StarMine credit risk model.

REINFORCED URN PROCESSES FOR MODELING CREDIT DEFAULT DISTRIBUTIONS

2004 ◽  
Vol 07 (04) ◽  
pp. 407-423 ◽  
Author(s):  
EMANUELE AMERIO ◽  
PIETRO MULIERE ◽  
PIERCESARE SECCHI
Keyword(s):  
Stochastic Model ◽  
Term Structure ◽  
Default Probability ◽  
Credit Spreads ◽  
Credit Default

Based on a Reinforced Urn Process introduced by Muliere et al. [11], we propose a stochastic model for the probability of credit default for debt issuers belonging to the same Moody's rated class. The model predicts how a default probability belonging to a given term structure evolves in time as information about credit defaults of debt issuers with the same Moody's rating becomes available. Connections between implied credit default probabilities and credit spreads will be exploited.

scholarly journals Volatility Timing: Pricing Barrier Options on DAX XETRA Index

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 722
Author(s):  
Carlos Esparcia ◽  
Elena Ibañez ◽  
Francisco Jareño
Keyword(s):  
Option Pricing ◽  
Term Structure ◽  
Barrier Options ◽  
Barrier Option ◽  
Probability Term ◽  
Volatility Timing ◽  
The Right ◽  
The Impact ◽  
Complementary Study ◽  
Frequency Current

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

ON SOME INCONSISTENCIES IN MODELING CREDIT PORTFOLIO PRODUCTS

2007 ◽  
Vol 10 (08) ◽  
pp. 1305-1321 ◽  
Author(s):  
FRANK J. FABOZZI ◽  
RADU TUNARU
Keyword(s):  
Credit Risk ◽  
Term Structure ◽  
Credit Rating ◽  
Risk Modeling ◽  
Main Concept ◽  
Rating Agencies ◽  
Probability Term ◽  
Credit Portfolio ◽  
Pricing Risk

The survival probability term structure has become the main concept in modeling credit risk for pricing, risk management, and investment decisions. The Kth-to-default contract is not only a relatively liquid credit risk instrument but also a vehicle that credit rating agencies employ to determine the rating of more esoteric credit risky positions. In this paper, we point out some subtleties in credit risk modeling of default baskets and also identify some potential bias in the pricing formula of the Kth-to-default contract. The numerical examples suggest that this bias increases with the correlation. The results in this paper emphasize the important role of conditioning the information regarding arrival of default.

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