PLEASE HELP !!! Heres an example :

The mean heating degree days in Pierre, SD is 1200, with a standard deviation of 200 for January. For February, it has a mean of 1300, with a standard deviation of 400. (Assume normal distribution for both.) What is the value of a call option on the sum of heating degree days in both months, with a strike price of 2200, when

A: The correlation between the two months is 0.5; B: when the correlation is -0.1.

Part A

The mean H for the 2 month strip is 2500. The variance is 200^2+ 400^2+ 2*200*400=40,000+160,000+160,000= 200,000+160,000.200^2+ 400^2+ 2*200*400=40,000+160,000+160,000= 200,000+160,000. When the =0.5, variance=280,000, standard deviation =sqrt(variance)=529.15. The strike price is 2200, so

X=(22002500)/529.15=0.567.Y=0.03X3+ 0.22X20.50X+0.4=0.76.X=(22002500)/529.15=0.567.Y=0.03X3+ 0.22X20.50X+0.4=0.76.

Price of derivative = std*Y=401.97.Price of derivative = std*Y=401.97.

Part B

When =-0.1, variance=184,000, std=428.95, X=-0.699, Y=0.868.

Price of derivative = std*Y=372.142. HERES THE QUESTION:

2) (70 points) Profits at Bangor Finestkind Power, Light, and Fishmarket (PFPL&F) for the winter of 2020-21 are expected to be

-84.5+0.23H-0.00012H², where H is the number of heating degree days in Bangor. H as a a normal distribution with a mean of 980 and a standard deviation of 230.

A: (5 points) What is the probability that PFPL&F will lose money next winter?

B: (10 points) You want to adopt a hedging strategy so that the probability of losing money because H is too low is 1.5 percent, while the probability of losing money because H is too high is 2 percent. What levels of H do you have to hedge to?

C: (10 points) Unhedged, what are the losses if H equals the levels you solved for in part B?

D: (10 points) Puts and calls are available at strike prices 0.7 standard deviations away from the mean, with a markup of 10 percent. How much will they cost?

E: (25 points) How many calls and puts will you purchase to hedge your position, as outlined in Part B?

F: (10 points) Graph your unhedged and hedged profits as H goes from 300 to 1600.