Term Structure of Credit Spreads
A credit curve is a graphical representation of the spread over benchmark security for an issuer of a credit risky bond across maturities. The following shows the term structure of credit spreads: The higher the time to maturity, the greater…
Interpreting Credit Spread
A corporate bond yield is made up of the benchmark yield and the credit spread. Benchmark yield The benchmark yield is affected by macroeconomic factors, including: The expected inflation rates. The expected real rate of return. Risk aversion for uncertainty…
Value of a Bond and its Credit Spread
The arbitrage-free framework is applied for credit analysis of a risky bond, assuming that interest rates are volatile. A binomial interest rate tree is constructed assuming no arbitrage. The tree is then verified if it has been correctly calibrated and…
Structural and Reduced Form Models
Structural Models Structural models focus on a firm’s assets and liabilities and define a mechanism for default. The probability of default is endogenous as default normally occurs when the value of the firm’s assets hits a barrier representing default. They…
Credit Migration
Credit rating agencies come up with transition matrixes of credit ratings based on the historical experience of issuers. A transition matrix captures the probability that a certain obligor will transition (migrate) from one credit state (rating) to another over a…
Credit Scores and Credit Rating
Credit scores and ratings are ordinal rankings used to classify credit quality. However, they do not explain the extent of the difference in quality between rankings. Credit Scores A credit score gives a snapshot of an individual’s credit risk at…
Measures of Credit Risk
Credit risk is the risk of default or delay in making interest or principal payments on a loan. On the other hand, credit spread is the difference between the yield to maturity of credit risky, zero-coupon bond, and a risk-free…
Valuation of a Convertible Bond in an Arbitrage Free Framework
Recall that according to the arbitrage-free framework, the value of a bond with an embedded option is equal to the sum of the arbitrage-free values of its parts. The arbitrage-free approach can be used to value convertible callable or putable…
Conversion Value
Conversion value (parity value) is the value of a bond if it is converted into common shares at the prevailing market price. $$ \text{Conversion value}=\text{Underlying share price} \times \text{Conversion ratio} $$ $$ \text{Minimum value of the convertible bond} = \text{max(Conversion…
Features of a Convertible Bond
A convertible bond is a hybrid instrument with a conversion option that gives the owner the right to convert debt into equity during a predetermined period (conversion period) at a predetermined price (conversion price). Investors can participate in the potential…
