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FRM Part I · FRM Exam Part I · Exotic Options

A volatility swap and a variance swap both have a volatility strike of 25 and a vega notional of USD 50,000. The volatility swap pays vega notional times (realized volatility minus strike). The variance swap pays vega notional/(2 × strike) times (realized variance minus strike variance). If realized volatility is 30, by how much does the variance swap payoff exceed the volatility swap payoff?

The variance swap pays USD 25,000 more. The volatility swap pays 50,000 × 5 = 250,000. The variance swap pays 1,000 × (900 − 625) = 275,000. The difference reflects the convexity of variance in volatility.

  1. AUSD 25,000Correct
  2. BUSD 275,000
  3. CUSD 50,000
  4. DUSD 12,500

Explanation

Volatility swap payoff = 50,000 × (30 − 25) = USD 250,000. Variance notional = 50,000/50 = 1,000, and the variance difference is 900 − 625 = 275, so the variance swap pays USD 275,000. The excess is 25,000, which matches N(σ−K)²/(2K) = 50,000 × 25 / 50. The 275,000 figure is the variance swap payoff alone, not the difference.

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