Explanation:
updated volatility estimate = [λ × (volatilityₜ₋₁)² + 1 − λ × (current return)²]⁰·⁵
λ = lambda (the weight of the previous volatility)
current return = ln(price today / price yesterday) = ln(42 / 48) = −13.353%
updated volatility estimate = [0.70 × (0.019)² + 0.30 × (−0.13353)²]⁰·⁵
updated volatility estimate = [0.0002527 + 0.005349078]⁰·⁵
updated volatility estimate = 7.48%
(Book 4, Module 49.3, LO 49.e)
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Question 34
An equity analyst is using an exponentially weighted moving average (EWMA) with a lambda of 0.70 to model the daily volatility of an equity security. The current estimate of daily volatility is 1.9%. The closing price of the equity was $48 yesterday and $42 today. Using continuously compounded returns, what is the updated estimate of volatility?
A
6.68%.
B
6.88%.
C
7.28%.
D
7.48%.
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