medium · FRM Part 1 Financial Markets and Products
A bank sells a 1-year European cap on a 3-month term reference rate struck at 4%, with quarterly caplets. The forward curve is flat at 4% and the bank delta-hedges each caplet. Suddenly the forward curve stays at 4% but the implied volatility surface steepens sharply, raising the vol of the longest-dated caplet far more than the shortest.
Which statement most accurately describes the change in the bank's exposure on a per-caplet basis, holding everything else fixed?
- All caplets sit exactly at the money with delta near zero, so the vega loss is identical for every single caplet and exposure just scales with caplet count
- The longest-dated caplet contributes the largest vega loss because at-the-money caplet vega rises with both time to expiry and the forward, dominating the steepening
- Vega is irrelevant for at-the-money caplets since option value is locally linear in volatility near the strike, so steepening produces no first-order P&L impact
- The shortest-dated caplet drives the entire loss here because its gamma is highest, and gamma and vega always move together, so high gamma must imply the largest vega exposure
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