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Q4. Delta and Gamma with Uniform Distribution (20 points) Current underlying price at 4,500, and you expect price at expiration follows uniform distribution with mean absolute deviation of 500. A customer wants to SELL 100x 5,000 strike CALL. You as a market maker is the counter party and you purchased 100x 5,000 strike CALL from the customer. Q4a. What is the TOTAL delta for your LONG CALL position? (2 points)

Q4b. How many shares do you need to long or short in order to offset the short collar position from above question Q4a? Do you long or short the underlying shares (2 points)?

Q4c. What is the total gamma value of your hedged long CALL position from Q4a and Q4b? (2 points)

Q4d. For the hedged long CALL position (long 100x CALLs, hedged with shares), what is the PnL from (starting) delta, and from gamma when underlying moves from 4500 to 4250? (4 points)

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Q4e. Calculate option prices when stock moves to $4250. How much of the total PnL of Q4d is from option position, and how much is from the stock position? (2 points)

Q4f. If underlying moves down from 4500 to 4250, what is the new delta at stock price of 4250 for your overall position based on gamma? If you need to re-hedge to flatten delta with underlying shares, what trade do you need to do in the shares to flatten the delta? (2 points)

Q4g. What is the PnL from the delta and gamma when underlying moves from 4500 to 4750, respectively? (2 points)

Q4h. For Q4g, how much of the total PnL is from option position, and how much is stocks, when underlying moves from 4500 to 4750? (2 points)

Q4i. Underlying moves up from 4500 to 4750. If you need to re-hedge to flatten delta with underlying shares, what trade do you need to do in the shares? (2 points)