FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A trader holds a long call option on a stock priced at USD 100 with delta 0.60. The stock's daily volatility is 2%. Using the delta-normal approximation, what is the one-day 99% VaR (z = 2.33) of the option position for 10,000 options?
The delta-normal VaR is USD 27,960. The position is equivalent to 0.60 times 10,000 shares worth USD 100 each, an exposure of USD 600,000. Multiplying by 2% daily volatility and the 2.33 z-value gives the VaR. Ignoring delta would overstate it.
- AUSD 27,960Correct
- BUSD 46,600
- CUSD 16,776
- DUSD 2,796
Explanation
Equivalent stock exposure = 0.60 x 10,000 x 100 = USD 600,000. Daily dollar volatility = 2% x 600,000 = USD 12,000. VaR = 2.33 x 12,000 = USD 27,960. The USD 46,600 option ignores delta (2.33 x 2% x 1,000,000). The USD 16,776 option applies delta twice (0.36 x 1,000,000 x 2% x 2.33).
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