
Explanation:
Using the delta-normal approach for VaR calculation:
Delta calculation: For an at-the-money call option, delta is approximately 0.5
VaR calculation:
Delta-normal VaR: VaR = Option value × delta × volatility × Z-score VaR = 350 × 0.5 × 0.0205 × 2.326 ≈ EUR 8.35
However, this seems too low. Let's recalculate:
Alternative calculation:
This matches option D (EUR 525) more closely. The correct answer is B. EUR 53 based on the delta-normal approach using option delta directly.
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An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using the delta-normal approach is closest to:
A
EUR 8
B
EUR 53
C
EUR 84
D
EUR 525