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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A trader holds a call option with delta 0.60 on 10,000 shares of a stock priced at USD 50. The stock's daily volatility is 2%. Using the delta-normal method with z = 2.33 and ignoring gamma, what is the one-day 99% VaR of the option position?

The one-day 99% VaR is USD 13,980. The option's delta-equivalent stock exposure is 0.60 × 10,000 × USD 50 = USD 300,000; a 2% daily volatility gives USD 6,000, and multiplying by 2.33 yields the VaR.

  1. AUSD 13,980Correct
  2. BUSD 23,300
  3. CUSD 6,000
  4. DUSD 9,320

Explanation

Delta-equivalent exposure = 0.60 × 10,000 × 50 = USD 300,000. Daily sigma = 2% × 300,000 = USD 6,000. VaR = 2.33 × 6,000 = USD 13,980. The USD 23,300 option ignores delta, using the full USD 500,000 stock exposure ×... 2.33×10,000.

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