FRM Part II · FRM Exam Part II · VaR Mapping
A risk manager holds a call option on 10,000 shares of a stock trading at $40. The option's delta is 0.55. The stock's daily return volatility is 2%. Using delta-normal mapping and a 95% one-day confidence level (z = 1.645), what is the approximate one-day VaR of the option position?
The one-day VaR is about $7,238. Delta-normal mapping converts the option into a stock position worth 0.55 × 10,000 × $40 = $220,000, and that exposure is multiplied by 2% volatility and the 95% z-value of 1.645.
- A$13,160
- B$5,922
- C$7,238Correct
- D$10,235
Explanation
Delta-normal mapping replaces the option with a delta-equivalent stock position: 0.55 × 10,000 × $40 = $220,000. VaR = 220,000 × 0.02 × 1.645 = $7,238. Omitting delta gives $13,160. Using 1 minus delta (0.45) gives $5,922. Using the 99% z-value of 2.326 gives $10,235.
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