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FRM Part II · FRM Exam Part II · Credit Value Adjustment

A bank trades an uncollateralized derivative with a corporate (asset position, expected positive exposure USD 20 million, constant over 3 years) and hedges it with a back-to-back collateralized trade with a dealer, where the bank must post cash collateral. The bank funds at a spread of 100 bps over the risk-free rate, and the collateral posted earns the risk-free rate. Assume the expected exposure to the corporate equals the collateral the bank must post on the hedge and that the funding spread applies to the full period. Approximately what is the FVA cost to the bank over the 3 years, ignoring discounting and default?

The FVA cost is about USD 600,000. The bank funds USD 20 million of posted collateral at a net spread of 1 percent, costing USD 200,000 per year, and over three years this totals USD 600,000 before discounting and default adjustments.

  1. AUSD 200,000
  2. BUSD 600,000Correct
  3. CUSD 60,000
  4. DUSD 2,000,000

Explanation

The bank must fund USD 20 million collateral at a 1% net spread (funding cost less risk-free return on collateral). Annual cost is 20,000,000 x 0.01 = USD 200,000, and over 3 years it is USD 600,000. USD 200,000 is one year only. USD 60,000 uses 0.1%. USD 2,000,000 uses 10 percent.

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