The CVA (Credit Valuation Adjustment) is the sum of the present value of expected losses across each period.

1. Hazard Rate ($\lambda$): The hazard rate is calculated as: $\lambda$ = CDS Spread / LGD. Since the counterparty's default probability follows a constant hazard rate process, we can check using any year:

• Year 1: $\lambda$ = 200 bps / (1 - 0.80) = 0.02 / 0.20 = 10% (0.10)
• Year 2: $\lambda$ = 300 bps / (1 - 0.70) = 0.03 / 0.30 = 10% (0.10)
• Year 3: $\lambda$ = 400 bps / (1 - 0.60) = 0.04 / 0.40 = 10% (0.10)

2. Probabilities of Default (PD): Using continuous compounding, the marginal probability of default for year $i$ is $PD_i = e^{-\lambda (i-1)} - e^{-\lambda i}$:

• $PD_1 = e^{-0} - e^{-0.10} = 1 - 0.90484 = 0.09516$
• $PD_2 = e^{-0.10} - e^{-0.20} = 0.90484 - 0.81873 = 0.08611$
• $PD_3 = e^{-0.20} - e^{-0.30} = 0.81873 - 0.74082 = 0.07791$

3. Discount Factors (DF): With a continuous risk-free rate of 3%:

• $DF_1 = e^{-0.03 \times 1} = 0.97045$
• $DF_2 = e^{-0.03 \times 2} = 0.94176$
• $DF_3 = e^{-0.03 \times 3} = 0.91393$

4. Net Exposure (EE): Net Exposure = Expected Positive Exposure - Collateral = 14 - 11 = 3 million AUD each year.

5. CVA Calculation:

• Year 1 CVA = 3 × 0.20 × 0.09516 × 0.97045 = 0.05539 million
• Year 2 CVA = 3 × 0.30 × 0.08611 × 0.94176 = 0.07299 million
• Year 3 CVA = 3 × 0.40 × 0.07791 × 0.91393 = 0.08544 million

Total CVA = 0.05539 + 0.07299 + 0.08544 = 0.21382 million $\approx`$0.21`4 million AUD.