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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A dealer's portfolio has delta 0, gamma -5,000 and vega -12,000 per 1 volatility point. A traded option has delta 0.50, gamma 2.0 and vega 8.0 per unit per volatility point. The dealer first uses the traded option to make the portfolio vega-neutral, then uses the stock to restore delta neutrality. Which trade is correct?

Buy 1,500 options and sell 750 shares. Buying 1,500 options offsets the minus 12,000 vega, but adds 750 of delta, which is neutralized by selling 750 shares. The stock has no vega, so the vega hedge is unaffected.

  1. ABuy 1,500 options and sell 750 sharesCorrect
  2. BBuy 1,500 options and buy 750 shares
  3. CSell 1,500 options and buy 750 shares
  4. DBuy 6,000 options and sell 3,000 shares

Explanation

Vega: -12,000 + 8n = 0 gives n = 1,500 options bought. Their delta is 1,500 x 0.50 = +750, so sell 750 shares to return to delta zero. Selling options would deepen negative vega; buying shares would add positive delta.

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