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

A trader holds 1,000 call options on a stock priced at USD 50. Each option has a delta of 0.60. The stock's daily volatility is 2% of its price. Using the delta-normal approach and a 99% one-day confidence level (z = 2.33), what is the VaR of the position?

The delta-normal VaR is USD 1,398. The stock's daily standard deviation is USD 1, so the 99% move is USD 2.33. Multiplying by 1,000 options and a delta of 0.60 gives the position's estimated worst one-day loss.

  1. AUSD 1,398Correct
  2. BUSD 2,330
  3. CUSD 987
  4. DUSD 932

Explanation

Daily standard deviation of the stock is 0.02 × 50 = USD 1.00. The 99% move is 2.33 × 1.00 = USD 2.33. VaR = 1,000 × 0.60 × 2.33 = USD 1,398. USD 2,330 omits delta; USD 987 uses the 95% z-value of 1.645; USD 932 uses (1 − delta) = 0.40.

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