FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A trader holds 1,000 long call options on a stock priced at $40. The option delta is 0.50. The stock's daily return volatility is 2%. Using the delta-normal approach and a 95% one-day confidence level (z = 1.645), what is the one-day VaR of the position?
The delta-normal VaR is $658. The position's delta-equivalent exposure is 0.50 x $40 x 1,000 = $20,000. Multiplying by 2% daily volatility gives $400, and multiplying by 1.645 for 95% confidence gives about $658.
- A$658Correct
- B$1,316
- C$930
- D$329
Explanation
Delta-normal VaR = delta x S x quantity x volatility x z = 0.50 x 40 x 1,000 x 0.02 x 1.645 = 20,000 x 0.02 x 1.645 = $658. Leaving out delta gives $1,316. Using the 99% z of 2.326 gives about $930. Applying delta twice gives $329.
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