Q4. Collar hedging (20 points) Underlying at $1000 and options have 2 weeks left before expiration (10 troding 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 980 strike. PUT is priced with an annual IV of $20; i. Long 100x call at 1020 strike. Call is priced with an annual IV of $15. Q4a, What are the deitas for each put and call contract? What is the total delta for the market maker's entire short collar position? (4 points) Q4b. How do you completely hedge 100x the delta exposure of the position with underlying shares? How many shares to long or to short? (1 point) Q4c. What is the gamma value for each put and call contract? What is the gamma value for market maker's overall short collar position (4 points)? Q4d. What is the daily theta of the short collar position? (1 point) Ris free rate of 0;252 trading days in a year; and Normal distribution for all questions For all questions in MT2 Q1. Underlying is trading at $1000. Binary CALL with strike of $850 with 16 trading days left is trading at 75c, What is the implied annual standard deviation? (10 points) Q2. Option Pricing (15 points) CAL Option has six months left before expiration. Underlying currently traded at 1000 with annual IV of 250 . CAL Strike is 800 . Q2a. What is the probability for cAut to expire in the money (5 points)? Q2.b. What is the average price of the underlying at expiration conditional on CALt expiring ITM (5 points)? Q2c. Based on Q2a, and Q2b, how much should the CALL be priced at today (3 points)? Q2d. Out of total call price from Q2e, how much is time value and how much is intrinsic value? (2 points) Q3. You short 100 ATM straddles with 28 trading days left. Underlying at $1000 currently, with annual IV of $300. (15 points) Q3a. What is the delta and gamma value of the position? (5 points) Q3b. What is the one-day theta value for the position? Is it positive or negative? (5 points) Q3C. If underlying goes down by $10 in one day, what is the delta / gamma / theta PnL, as well as the total PnL for the position? (5 points)? (hint; total PnL is the sum of PnL from a. delta; b. gamma; c. theta) Q4e. Underlying sold off from 1000 to 990 in one day. What is the delta and gamma PnL for your hedged short collat position from Q4b ? What is the total PnL including theta? (3 points) Q4f. If you want to flatten your delta (to stay delta neutral) after stock priced sold from 1000 to 990 , how do you rehedge your delta? le how many shares do you need to buy or sell? (2 points) Q4e. Underlying rallied from 1000 to 1015 in one day. What is your delta / gamma/ theta PnL as well as the total Pol for the hedged collar position from QQ4b? (3 points) Qth. If vou want to flatten your detta fto stay delta nevitral) after stock priced rallied from 1000 to 1015 , how do you rehedge your delta? le how many shares do you need to buy or sell? (2 points)
