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Answer: USD 557
## Explanation Using the delta-normal approach for VaR calculation: 1. **Calculate the 1-day 95% VaR for 1 share of the underlying stock:** - Daily volatility (σ) = 1.82% = 0.0182 - Z-score for 95% confidence level = 1.645 - Current stock price = USD 62 - VaR per share = σ × Z × Stock Price = 0.0182 × 1.645 × 62 = USD 1.8562 2. **Calculate VaR for one option:** - Delta (Δ) = 0.5 - VaR per option = Δ × VaR per share = 0.5 × 1.8562 = USD 0.9281 3. **Calculate VaR for the entire position:** - Number of options = 600 - Total VaR = VaR per option × Number of options = 0.9281 × 600 = USD 556.86 ≈ USD 557 **Why other options are incorrect:** - **A (USD 54)**: Ignores delta and uses option price instead of stock price - **C (USD 787)**: Uses 99% confidence level (Z = 2.326) instead of 95% - **D (USD 1,114)**: Forgets to apply delta to the calculation
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A portfolio manager bought 600 call options on a non-dividend-paying stock, with a strike price of USD 60, for USD 3 each. The current stock price is USD 62 with a daily stock return volatility of 1.82%, and the delta of the option is 0.5. Using the delta-normal approach to calculate VaR, what is an approximation of the 1-day 95% VaR of this position?
A
USD 54
B
USD 557
C
USD 787
D
USD 1,114