Q3. Stock at 100. 63 DTE. 1Y IV is $40. Consider OTM put with 80 strike.

a. what is the option delta and gamma and theta?

b. if you sold 500 put contracts, and each contract has a multiplier of 100, how do you hedge your position with underlying shares?

c. after you put on position from Q3b, market did not move and there are now 16 days left. What is the option position's delta now? how do you adjust your hedge to stay delta neutral?

d. market immediately rallied by 1% after you put on the position from Q3b. There are still 63 days left. If IV stays the same, what is your new delta due to gamma effect? How should you adjust your hedge?

e. Stock did not move and option's IV dropped by 4 points from 40 to 36 annually. Still 63 days DTE. What is your new delta? How should you adjust your hedge position?