Q3. Collar hedging Underlying at 100 and options have 2 weeks left before expiration (10 trading days). Long PUT and short CALL is known as a long collar position. As an option market maker you have the following short collar position: i. Short 100x put at 95 strike. PUT is priced with an annual IV of $30; ii. Long 100x 105 delta call. Call is priced with an annual IV of $20. Q3a. What are the deltas of the put and the call for each put and call? What is the total delta for the 100x short collar position? How do you hedge the delta of the position with underlying shares? How many shares to long or to short?

Q3b. What is the gamma value of the short collar position? What is the daily theta of the position?

Q3c. Underlying makes a sudden $5 dive one day, going from 100 to 95. What is the delta and gamma PnL FOR your HEDGED SHORT COLLAR position from Q3a? What is the total PnL including theta?

Q3d. Re-calculate delta for the hedged collar position after the stock price moved down to 95. Assume 95 PUT IV stays at 30 and 105 CALL IV stays at 20. If you want to flatten your delta (to stay delta neutral), how do many incremental shares do you need to buy or sell? (hint: new delta calculation needs to take into account that the collar now has 9 days left. Plug in new underlying and new DTE to the delta formula for PUT and CALL instead of using gamma approximation)

Q3e. Re-calculate delta for the hedged collar position after the stock price moved up to 105. Assume 95 PUT IV stays at 30 and 105 CALL IV stays at 20. If you want to flatten your delta (to stay delta neutral), how do many incremental shares do you need to buy or sell?

Please, show a work