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P2.T5.507. Credit and debit value (CVA and DVA) adjustments and the risk-free rate

Nicole Seaman

Director of FRM Operations
Staff member
Learning outcomes: Explain why the OIS rate is a good proxy for the risk-free rate. Describe how to construct the OIS zero curve, and using it, determine forward LIBOR rates.


507.1. A company with an average funding cost of 4.0% is currently undertaking projects worth $80.0 million. The risk-free rate is 2.0%. The company has the opportunity to undertake an additional $20.0 million project. The additional project, remarkably, is itself risk-free but returns only 3.0%. Should the company undertake the additional project?

a. No, because the project's return does not exceed its average funding cost
b. No, because a riskless project by implication has a net present value (NPV) of zero
c. Yes, the project's return exceeds the risk-free rate and the company's average funding cost will decrease to 3.60%
d. Yes, the project's return exceeds the risk-free rate but the company's average funding cost will be unchanged

507.2. The credit spread of a bank increases suddenly to reflect that its default probability has increased. What happens to the bank's debt (or debit) value adjustment (DVA) and its reported income?

a. DVA decreases with no impact to reported income
b. DVA increases and reported income decreases
c. DVA increases with no impact to reported income
d. DVA increases and reported income increases

507.3. In regard to CVA, DVA, FVA and the collateral rate adjustment, each of the following is true EXCEPT which is false, at least according to Hull? (Hull, Options, Futures, and Other Derivatives, Pearson; 9 edition (January 25, 2014))

a. The credit value adjustment (CVA) measures the cost to a derivatives market participant because its counterparty might default
b. The debt value adjustment (DVA) measures the benefit to a market participant (which equals the cost to the counterparty) because the market participant itself might default
c. The collateral rate adjustment is an adjustment made if the interest paid on collateral is different from the assumed risk-free rate
d. A funding value adjustment (FVA) is theoretically correct and necessary because the value of investment is certainly a function of its funding costs

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