Question

Q4. You observed a stock moves 2% stdev each day usually, except for days of earning announcement. In the latter case, it has a stdev of 10%. Today is a Friday. You are interested in an option that expires in FOUR weeks. Earning announcement will be on the next Friday.

Q4a. What should be annualized IV now? (4 points)

Q4b. On next Thurday at close, what should be IV? (3 points)

Q4c. On Friday at close, just after ER, what should be IV? (3 points)

Answer 1

IV (Implied Volatility) refers to the standard deviation on stock price movement. In case of an option, we calculate IV as follows:

IV = Standard Deviation % x (365 / Days to expire)(1/2)

(assuming days in an year are 365)

This helps us in determining the risk component of a stock.

(A) Today is Friday, and the standard deviation is 2%.

IV = Standard Deviation x (365 / Days to expire)1/2
= 2% x (365 / (7*4))1/2 (given there are 4 weeks to expire x 7 days in 1 week)
=2% x (13) 1/2 = 2% x 3.6 = 7.2%

(B) Next Thursday at close, the standard deviation would still be at 2%, since IV changes to 10% on days of Earning Announcement

Therefore, IV (formula given above) = 2% x (365 / 21) ½ (since 21 days are left to expiration of option, as 7 days would have passed since Friday on Thursday close)
= 8.3 %

(C) On Friday at close, after the announcement, the standard deviation would be 10% for 1 day. We know that the standard deviation touches 10% for 1 day and then comes back to 2% for remaining 19 days (since 20 days are left to expiration of option, as 1 day passed since Thursday close).

Therefore, average standard deviation = ((10% x 1) + (2% x 19)) / 20
= (10% + 38%)/20 = 48%/20 = 2.4%

Now, IV on 2.4% Standard deviation for 20 days will be

IV = 2.4% x (365 / 20)1/2
= 2.4% x (18.3)1/2
=2.4% x 4.3 = 10.3%