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FRM Part I · FRM Exam Part I · Exotic Options

A fund buys a variance swap with a vega notional of USD 100,000 and a volatility strike of 20. The variance notional is defined as vega notional divided by twice the volatility strike, and the payoff is variance notional times (realized variance minus strike variance), with variances in squared volatility points. Realized volatility at maturity is 24. What is the payoff to the fund?

The payoff is USD 440,000. The variance notional is 100,000 / 40 = 2,500 per variance point. Realized variance of 576 exceeds strike variance of 400 by 176, and 2,500 × 176 equals 440,000.

  1. AUSD 440,000Correct
  2. BUSD 400,000
  3. CUSD 10,000
  4. DUSD 880,000

Explanation

Variance notional = 100,000 / (2 × 20) = 2,500 per variance point. Realized variance = 24² = 576 and strike variance = 20² = 400, a difference of 176. Payoff = 2,500 × 176 = USD 440,000. Vega notional × 4 gives 400,000, which wrongly treats the swap as a volatility swap. Using vega/K as the notional doubles the payoff to 880,000.

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