Delta and Gamma with Uniform Distribution:

Current underlying price at 100, and you expect price at expiration follows uniform distribution with mean absolute deviation of 20. You short 10 PUTs with strike at 80.

Q1a. For the hedged put position (short 10 puts, hedged with shares), what is the PnL from (starting) delta, and from gamma when underlying moves from 100 to 80, respectively?

Q1b. Calculate option price when stock moves $80. How much of the total PnL of Q4d is from option position, and how much is from the hedging position using stocks, when underlying moves from 100 to 80?

Q1c. If underlying moves down from 100 to 80, what is the new delta at stock price of 80 for your overall position based on gamma? Recalculate the portfolio delta using option delta expression to confirm gamma approximation is accurate.? 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?

Q1d. What is the PnL from the total delta and gamma when underlying moves from 100 to 120, respectively?

Q1e. From Q1c, how much of the total PnL is from option position, and how much is from the hedging position using stocks, when underlying moves from 100 to 120?

Q1f. If underlying moves up from 100 to 120, If you need to re-hedge to flatten delta with underlying shares, what trade do you need to do in the shares?