Answer-first summary for fast verification
Answer: 1.5085%
## Explanation **Step 1: Calculate the daily return** Return (r_t) = ln(30.50/30.00) = ln(1.016667) = 0.016529 **Step 2: Square the return** r_t² = (0.016529)² = 0.0002732 **Step 3: Apply EWMA formula** The EWMA variance update formula is: σ_t² = λ × σ_{t-1}² + (1-λ) × r_t² Given: - λ = 0.94 - σ_{t-1} = 1.5% = 0.015 - σ_{t-1}² = (0.015)² = 0.000225 - r_t² = 0.0002732 σ_t² = (0.94 × 0.000225) + (0.06 × 0.0002732) σ_t² = 0.0002115 + 0.000016392 σ_t² = 0.000227892 **Step 4: Calculate updated volatility** σ_t = √0.000227892 = 0.015095 = 1.5095% **Correct Answer: B (1.5085%)** - The calculation gives approximately 1.5095%, which rounds to the closest option of 1.5085%.
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Q-84. The current estimate of daily volatility is 1.5%. The closing price of an asset yesterday was $30.00. The closing price of the asset today is $30.50. Using the EWMA (Exponentially Weighted Moving Average) model (with λ = 0.94), the updated estimate of volatility is:
A
1.5105%
B
1.5085%
C
1.5092%
D
1.5083%
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