scholarly journals Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2033
Author(s):  
Zhehao Huang ◽  
Zhenghui Li ◽  
Zhenzhen Wang

Credit risk modeling by debt pricing has been a popular theme in both academia and practice since the subprime crisis. In this paper, we devote our study to the indifferent price of a corporate bond with credit risk involving both default risk and credit rating migration risk in an incomplete market. The firm’s stock and a financial index on the market as tradable assets are introduced to hedge the credit risk, and the bond price is determined by the indifference of investors’ utilities with and without holding the bond. The models are established under the structural framework and result in Hamilton–Jacobi–Bellman (HJB) systems regarding utilities subject to default boundary and multiple migration boundaries. According to dynamic programming theory, closed-form solutions for pricing formulas are derived by implementing an inverted iteration program to overcome the joint effect of default and multiple credit rating migration. Therefore, with the derived explicit pricing formulas for the corporate bond, the models can be easily applied in practice, and investors can generate their strategies of hedging the credit risk by easily analyzing the impacts of the parameters on the bond price.

2007 ◽  
Vol 10 (03) ◽  
pp. 557-589 ◽  
Author(s):  
MAREK RUTKOWSKI ◽  
NANNAN YU

The innovative information-based framework for credit risk modeling, proposed recently by Brody, Hughston, and Macrina, is extended to a more general and practically important setup of random interest rates. We first introduce the market model, and we derive an explicit expression for defaultable bond price. Next, the dynamics of the information process and dynamics of defaultable bond are found for both deterministic and random interest rates. Finally, the valuation and hedging of derivative securities are briefly examined. In particular, the valuation formula for a European option on a defaultable bond is established.


2019 ◽  
Author(s):  
Tim Xiao

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, and how CDS spreads depend on the trilateral credit risk of the buyer, seller, and reference entity in a contract. Moreover, we study the effect of collateralization on valuation, since the majority of OTC derivatives are collateralized. The model shows that a fully collateralized swap is risk-free, whereas a fully collateralized CDS is not equivalent to a risk-free one.


2012 ◽  
Vol 20 (3) ◽  
pp. 325-346
Author(s):  
Seung Hyun Oh

This study investigates the relation between two kinds of par yield curves estimated in Korean bond market: benchmark par yield curve and company par yield curve. The former is published as a benchmark for corporate bonds with a given credit rating and the latter is utilized for valuing a specific corporate bond. Spot rate curves are extracted from the par yield curves by applying bootstrapping method. The spreads between the two spot rate curves are analyzed for 7 years (2005~2012) of corporate bond transaction data. Six results are obtained from various sub-samples classified by credit rating and maturity. 1) Most of the sample means of the spreads are above zero. 2) Negative average spreads are found mainly from the sample of BBB rated bonds. 3) Average spreads from the sample with credit greater than or equal to A tend to positively related with credit risk. 4) Absolute value of the average spreads are positively related with credit risk. 5) The average spreads are increased rapidly after the year of 2009. 6) The proportion of sub-samples having negative average spreads are decreased as the average maturity of the sample is shortened.


Author(s):  
Tim Xiao

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, and how CDS spreads depend on the trilateral credit risk of the buyer, seller, and reference entity in a contract. Moreover, we study the effect of collateralization on valuation, since the majority of OTC derivatives are collateralized. The model shows that a fully collateralized swap is risk-free, whereas a fully collateralized CDS is not equivalent to a risk-free one.


2013 ◽  
Vol 655-657 ◽  
pp. 2258-2261
Author(s):  
Jie Min Huang ◽  
Su Sheng Wang ◽  
Jing Xia Xu ◽  
Zhao Hua Lan

Foreign literatures are mainly about analyst forecast dispersion, liquidity risk, equity market volatility, default risk, taxes, credit risk, and the interaction of credit risk and default risk and other factors that influence bond spread. The literatures including the research on the impact of equity market index, but little literatures refer to the impact of bond complex index on bond spread. There are different opinions about the impact of systemic risk on bond spread


2007 ◽  
Vol 10 (08) ◽  
pp. 1305-1321 ◽  
Author(s):  
FRANK J. FABOZZI ◽  
RADU TUNARU

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.


2020 ◽  
Vol 15 (4) ◽  
pp. 371-388
Author(s):  
Henry Penikas

The Basel Committee on Banking Supervision finalized the Basel III accord in the December 2017 and launched the set of its standards – the Basel Framework – in December 2019. Both documents allow bank to use mathematical models for the credit risk estimation. There are quantitative and qualitative requirements for models to be allowed for use in the prudential regulation of banks. The approach is called an Internal-Ratings-Based one (IRB). This paper aims at discussing a set of issues related to IRB credit risk modeling and such model estimates use. Those issues include data pooling in the credit registries, applying copula-discriminant analysis, validating the borrower concentration per grade, assigning the hybrid credit rating, use of model estimates when voting at the credit committee, estimate of the ultimate credit risk-taking by banks.


Accurate assessment of credit risk can improve the performance of bond portfolio managers. Using credit ratings and market-based credit risk models from S&P and Bloomberg, we investigate the performance of four credit risk models in the Rule 144A corporate bond markets in the United States over the 1990–2015 period. The authors divide their sample into straight bonds and convertible bonds and find that (1) when it comes to straight bonds, discrete models such as S&P’s credit ratings and Bloomberg ratings determine yields more accurately than the continuous market-based models of S&P and Bloomberg; (2) with regard to convertible bonds, a convertible option has a stronger effect than credit ratings in determining yields, and only Bloomberg default risk ratings, not S&P credit ratings, determine the yields; (3) for convertible bonds, the continuous market-based models of S&P and Bloomberg affect yields more significantly than discrete models; and (4) when it comes to predicting actual defaults, Bloomberg models are superior to S&P’s models, and the Bloomberg discrete model has more power than its continuous counterpart.


2018 ◽  
Vol 94 (1) ◽  
pp. 299-326 ◽  
Author(s):  
Mani Sethuraman

ABSTRACT This paper explores the effect of a credit rating agency's (CRA) reputation on the voluntary disclosures of corporate bond issuers. Academics, practitioners, and regulators disagree on the informational role played by major CRAs and the usefulness of credit ratings in influencing investors' perception of the credit risk of bond issuers. Using management earnings forecasts as a measure of voluntary disclosure, I find that investors demand more (less) disclosure from corporate bond issuers when the ratings become less (more) credible. In addition, using content analytics, I find that bond issuers disclose more qualitative information during periods of low CRA reputation to aid investors in assessing credit risk. My findings are consistent with credit ratings providing incremental information to investors and reducing adverse selection in lending markets. Further, consistent with theoretical predictions, my findings suggest that managers rely on voluntary disclosure as a credible mechanism to reduce information asymmetry in bond markets.


Author(s):  
I. Hanus ◽  
I. Plikus ◽  
T. Zhukova

IFRS 9 “Financial Instruments” introduced a new model of impairment based on expected credit losses, in which the impairment is based on expected credit losses, and the provision for losses is recognized before the credit loss, i.e. companies recognize losses immediately after initial recognition of the financial asset and revise the amount of the provision for expected credit losses at the reporting date. To create a provision for credit losses, IFRS 9 allows using several practical tools, including the rating debtors’ method. However, IFRS 9 does not express a clear opinion on how the expected credit loss for receivables should be calculated. In this regard, in our opinion, it is possible to apply an individual approach to the choice of credit risk assessment method, determining the debtor’s credit rating and the choice of the default probability, and so on. The paper substantiates that the debtors’ rating by the level of corporate default risk is a method that can reliably assess the probable risks. This method uses credit ratings. The paper proposes using the international credit ratings, which will allow a more objective creditworthiness assessment of both foreign and domestic debtors, taking into account macroeconomic factors used by rating agencies to determine the class of credit risk. The article presents the credit rating of Ukraine and changes in the credit rating of Ukraine for 15 years (2004-2019), shows the model of applying the international default probability rates. Two variants of applying this model are offered. Under the first option, the total amount of receivables from the counterparty / group of debtors is multiplied by the percentage of default probability. The second option involves applying the selected ratio according to the credit rating class at the last stage of calculating the expected credit losses by the simplified method. Due to the fact that there is no single approach to choosing the probability of default and everything relies on expert opinion, we propose using the data of the Annual Global Corporate Default And Rating, which is an analysis of market conditions in the world, the corporate defaults overview, the coefficient of bankruptcy probability of economic entities for each of the risk groups. The paper proposes using the annual rate of corporate defaults, as the expected credit losses must be calculated by companies on a regular basis and revalued at least once a year (on the balance sheet date). It is substantiated that the use of the average rate (Average Rate) to assess the probability of default, it is this rate that takes into account the past experience of companies that are in the corresponding zone of default risk for all the periods under consideration.


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