Disclaimer: Definitions have been cited from Investopedia.

What is Credit Risk?

â€œThe risk of loss of principal or loss of a financial reward stemming from a borrower’s failure to repay a loan or otherwise meet a contractual obligation. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. Investors are compensated for assuming credit risk by way of interest payments from the borrower or issuer of a debt obligation.â€

What is Counter Party Risk?

â€œThe risk to each party of a contract that the counterparty will not live up to its contractual obligations. Counterparty risk as a risk to both parties and should be considered when evaluating a contract.

In most financial contracts, counterparty risk is also known as "default risk".â€

### Book Value and Market Value of Capital Structure

Book value refers to the accounting balance sheet, where the assets, debt and equity are present in book (historical value).

Economic balance sheet contains the market value of the various capital structure components

Where

Et = Market value of equity

At = Market value of assets

### Expected Loss

Expected loss is the average value of the credit loss. Provisions are set aside to cover these losses.

### When will Investor Invest in Risky Bond?

The investor will invest in risky bond if the expected return from risky bond is more than the return from a risk free bond on risk adjusted basis.

Let r% be the return from risk free bond.

Let z% be the credit spread for risky bond. Therefore the expected return on risky bond is r%+z%.

Let PD be the probability of default of the risky bond.

Let RR be the recovery rate from the risky bond in case of default.

### Merton Model

If the firm is unable to pay the principal at time T, then it is bankrupt and equity holders will not get anything.

If the value of the firm at time T is VT which is large enough to pay the principal, then the equity holders will get the balance i.e. VT â€“ F

In Merton model, the payoff for equity holders is same as the payoff for a long call option.

The payoff for the debt holder is same as that of the risk free bond and short position in put option.

At the time of maturity, if the VT > F, then the debt holders will receive F.

At the time of maturity, if the VT < F, then the debt holders will receive VT and their payoff will be reduced by F – VT.

### Credit Factor Models

Factor models relate the risk of credit loss to fundamental economic quantities.

A single factor model can be used to value a firm’s asset returns.

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