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

credit spread = yield to maturity of a risky bond - yield to maturity of a government bond
Its value includes default probability, loss given default, time value of money, and the risk premium. A credit risk model can help us understand each of these components.

To model credit risk, a few factors need to be considered:
1. Expected exposure measures how much the investor could lose if default occurs, before considering any possible recovery.

2. 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.

Consider a 1-year, 4% annual payment corporate bond priced at par. Its expected exposure is \$104. Assume a 40% recovery rate, and it applies to both interest and principal. The loss given default is 104 x (1 - 0.4) = 62.4.

3. Probability of default addresses the likelihood that a borrower will default on its debt obligations, without reference to estimated loss.

Note that 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.

The preferred measure is to calculate 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): POSi - PODi+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.

User Comment
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” 