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FRM Part I · FRM Exam Part I · Exotic Options

A trader is long a variance swap struck at a volatility of 20%. Realized volatility over the life of the swap turns out to be 10 volatility points above the strike in one scenario and 10 points below the strike in another. Which statement about the long position's payoff is correct?

The gain is larger in absolute size than the loss. A variance swap pays on squared volatility, so its payoff is convex in volatility. A rise of 10 points above the strike adds more variance than a fall of 10 points below it removes.

  1. AThe gain in the first scenario is larger in absolute size than the loss in the secondCorrect
  2. BThe gain in the first scenario equals the loss in the second in absolute size
  3. CThe gain in the first scenario is smaller in absolute size than the loss in the second
  4. DThe long position can never lose money if realized volatility is positive

Explanation

The variance swap payoff is proportional to realized variance minus strike variance, which is convex in volatility. At 30% the variance difference is 900 − 400 = 500. At 10% it is 100 − 400 = −300. The gain is therefore larger than the loss, so equal gains and losses are wrong.

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