Market risk, Credit risk and default probabilities

Q: What is the difference between market risk and credit risk?

A: Market risk is a systematic risk to which any FI exposed. While the credit risk is a probability of default by borrowers or counterparties in a derivatives transaction.

Q: What are the methods for calculating these risks?

A: Market risk is calculated using VaR and Greek letters like Gamma, Vega and Theta etc. While the default probabilities for credit risk are calculated using historical data or Bond prices/Equity prices. The default probabilities calculated from historical data are real-world probabilities. While those calculated from bond prices/equity prices are called risk-neutral probabilities.

Q: Are these two probabilities different and if yes then why?

A: Yes, they are different because of the presence of expected excess returns over the risk free rate. If there were no expected excess return then the two probabilities would be same.