Explanation

Using the delta-normal method for VaR calculation:

Given:

• Stock price (S) = USD 23
• Daily volatility (σ) = 1.5% = 0.015
• Delta (Δ) = -0.5 (for long put position)
• Confidence level = 95% (z-score = 1.645)
• Holding period = 1 day

VaR formula for options using delta-normal method: $\text{VaR} = |\Delta| \times S \times \sigma \times z$

Calculation: $\text{VaR} = |-0.5| \times 23 \times 0.015 \times 1.645$ $\text{VaR} = 0.5 \times 23 \times 0.015 \times 1.645$ $\text{VaR} = 0.5 \times 0.345 \times 1.645$ $\text{VaR} = 0.1725 \times 1.645$ $\text{VaR} = 0.2837$

Result: USD 0.2837 ≈ USD 0.28

Key points:

• The absolute value of delta is used because VaR represents potential loss
• For a long put position, the risk comes from the stock price increasing (which decreases put value)
• The delta-normal method linearizes the option's risk using delta as the sensitivity measure
• The 95% confidence level corresponds to a z-score of 1.645 for one-tailed normal distribution