What is the EWMA estimate of the volatility the next day?

A stock’s volatility under EWMA is estimated at 3.5% on a day its price is $10. The next day, the price moves to $11.

What is the EWMA estimate of the volatility the next day? Assume the persistence parameter = 0.93.

A. 0.0421

B. 0.0224

C. 0.0429

D. 0.0018

Answer: A

Explanation:

The correct answer is choice ‘a’

Recall the formula for calculating variance under EWMA. See below. Therefore the correct answer is =SQRT ((1 – 0.93) *(LN (11/10))^2 + 0.93*((3.5%^2))) = 4.21%. Other answers are incorrect. Note that continuous returns are to be used, ie ln (11/10) and not discrete returns (=1/10) – though generally the difference between the two is small over short time periods. (If in the exam the answer doesn’t exactly match, try using discrete returns.)