Monte Carlo Methods for Risk Management: CVA and the Merton Model in Python

1. Exposure to Default and CVA

Credit Valuation Adjustment, or exposure, is what, at any time t, you are at risk of losing, if the counterparty were to default.

It is the higher of the value of the portfolio and 0, i.e.

• If your portfolio has a negative value (meaning you would owe the other party money), and they default, you don’t lose out on any profit.
• If the value of the portfolio was positive and they defaulted, you would lose the value of the portfolio (the amount they owed you).

Different Types of Exposure:

• Current exposure, which is the exposure when t is the current time
• Expected Exposure, which is what you predict the exposure to be at a future time t
• Potential Future Exposure, the confidence level on exposure at some future time (similar to VaR)

Definition of Credit Valuation Adjustments

CVA is calculated as the difference between the value of a portfolio which we assume is risk-free, and a portfolio where we account for default risk.