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.

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

b. On next Thursday at close, what should be IV? (3 points)

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

Answer 1

a. Annualised IV now

IV stands for 'Implied Volatility'. This is a metric used by investors to forecast the likely movement in a security's price based on certain predictive factors.

Standard Deviation of daily stock movement can be represented in the following equation:

Standard Deviation of daily movement = Implied Volatility * square root of days to expiration / square root of 365

Thus, implied volatility = Standard Deviation of daily movement * square root of 365 / square root of days to expiration

Here, Standard Deviation of daily stock movement = 2%

Days to expiration =  Expiry in 4 weeks, sence 7 days in a week * 4 weeks = 28 days

365 = to identify the annualised IV (considering 365 days in a year)

IV =2%*(365^(1/2))/(28^(1/2)) = 2%*19.105/5.292 = 2%*3.611 = 7.22%

Thus, Annualised IV now = 7.22%

b. IV on next thursday close

Earning announcement is next friday, hence thursday still has usual stock movement standard deviation of 2%.

Since the calculation on IV is on next thursday, the days to expiration reduces by a week, thus, revised days of expiry = (4 weeks * 7 days) - (1 weeks * 7 days) = 21 days

Using the same equation of IV as above,

IV on next thursday = 2%*(365^(1/2))/(21^(1/2)) = 2%*19.105/4.583 = 2%*4.169= 8.34%

IV on next thursday close = 8.34%

c. IV on friday, after earnings announcement

The days to expiration (on friday) will further reduce by 1 day = 21 days - 1 day = 20 days

Stock movement standard deviation is 10% on earning announcement days and 2% on other days , thus average standard deviation for 20 days = (10% * 1 day + 2% * 19 days) / 20 = (0.1+.38)/20 = 0.48/20 = 0.24 or 2.4%

Using the same equation of IV as above,

IV on friday after earnings announcement = 2.4%*(365^(1/2))/(20^(1/2)) = 2.4%*19.105/4.472 = 2.4%*4.272= 10.25%

IV on friday after earnings announcement = 10.25%