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

A bank has an interest rate swap in which it receives fixed from a counterparty. Assume the counterparty is the only defaultable party. How does the unilateral CVA on this trade compare with that on an otherwise identical trade with a longer maturity, all else equal?

The longer-maturity swap normally has higher unilateral CVA. Expected exposure builds as rates move, and a longer horizon accumulates more counterparty default probability. CVA therefore depends on exposure profile and default timing, not just notional, and zero initial value does not mean zero CVA.

  1. AIt is typically lower for the longer trade because exposure decays
  2. BIt is identical because CVA depends only on the notional amount
  3. CIt is typically higher for the longer trade because of greater potential exposure and longer default horizonCorrect
  4. DIt is zero for both because swaps have no exposure at inception

Explanation

For a swap, expected exposure usually grows with time due to rate diffusion before amortisation effects, and a longer horizon adds more cumulative default probability. Thus CVA generally rises with maturity. Notional alone does not determine CVA, and a zero-value start does not imply zero future exposure.

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