- CFA Exams
- 2025 Level II
- Topic 6. Fixed Income
- Learning Module 29. Credit Analysis Models
- Subject 1. Modeling Credit Risk and the Credit Valuation Adjustment

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##### Subject 1. Modeling Credit Risk and the Credit Valuation Adjustment PDF Download

**Default risk**addresses the likelihood that a borrower will default on its debt obligations, without reference to estimated loss.

**Credit risk**considers both the default probability and how much is expected to be lost if default occurs.

To model credit risk, a few factors need to be considered:

**Expected exposure**measures how much the investor could lose if default occurs, before considering any possible recovery.- If a bond defaults, investors can still expect to recover a certain percentage of the bond, and that percentage is called the
**recovery rate**.**Loss given default (LGD)**measures the portion of value an investor loses. **Probability of default**addresses the likelihood that a borrower will default on its debt obligations, without reference to estimated loss.*risk-neutral probabilities*instead of actual default probabilities should be used. Risk-neutral probabilities are probabilities of potential future outcomes adjusted for risk, which are then used to compute expected asset values.

*present value of the expected loss*.

There is no need to repeat the comprehensive textbook example here. A few hints:

- (2) Exposure: This is the present value of the bond discounted using the risk-free rate, at time T.
- (3) Recovery: (2) x 40%.
- (4) Loss given default (LGD): (2) - (3)
- (5) Risk Neutral Probability of Default (POD): it is the conditional probability of default.
- (6) Probability of Survival (POS): POS
_{i}- POD_{i+1} - (7) Expected Loss: (4) x (5)
- (8) Risk-Free Discount Factor (DF):
- (9) PV of Expected Loss: (7) x (8)

The

**credit valuation adjustment (CVA)**is calculated as the sum of the present values of the expected loss for each period in the remaining life of the bond.

- Depending on the timing of default, the range of outcomes can be very wide.
- The CVA can be expressed in terms of a credit spread.

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**User Contributed Comments**
2

User |
Comment |
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Allen88 |
Expected loss can be updated, the grammar seems a bit off. Loss Given Default = Full Amount owed - Expected Recovery. |

Yarrstar |
“LGD is often expressed as the percentage of the position or exposure” |

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