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. $$ \text{Conversion value}=\text{Underlying share price} \times \text{Conversion ratio} $$ $$ \text{Minimum value of the convertible bond} = \text{max(Conversion…
Features of a Convertible Bond
A convertible bond is a hybrid instrument with a conversion option that gives the owner the right to convert debt into equity during a predetermined period (conversion period) at a predetermined price (conversion price). Investors can participate in the potential…
Capped or Floored Floating-Rate Bonds
Capped and floored floaters can be valued using the arbitrage-free framework. Valuation of a Capped Floater A capped floater (floating rate loan) is a bond that pays a coupon that resets every period based on the reference rate. Reference rates…
Effective Convexities
Effective convexity is the sensitivity of duration to changes in interest rates. $$ \text{Effective convexity} =\cfrac {P_{i-}+P_{i+}-2 \times P_o}{P_0 (\Delta \text{Curve})^2} $$ Both callable and straight bonds experience similar positive convexity when interest rates are high. However, the effective convexity…
One-Sided Durations and Key Rate Duration
One-sided Duration Bonds with embedded options have asymmetrical price sensitivity to up or down interest rate movements of the same magnitude. When the embedded option is in the money, the price of a callable bond has limited upside potential, while…
