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For all questions below, assume :

rf=0; (b). sigma_1y = $20. S0=100.

Q1a. Calculate price of a 1 month PUT with S0 =100, while varying strike price b/w 60 and 140

Q1b. Calculate price of a 3 month PUT with S0 =100, while varying strike price b/w 60 and 140

Q1c. Calculate price of a 12 month PUT with S0 =100, while varying strike price b/w 60 and 140

Q1d. Graph a-c in the same chart. x-axis is the strike price. y-axis is the PUT price.

2a. Calculate the delta of 3 month PUT with S0=100, while varying strike X from 80 to 120

2b. Calculate the delta of 12 month PUT with S0=100, while varying strike X from 80 to 120

2c. Calculate the delta of 3 month CALL with S0=100, while varying strike X from 80 to 120

2d. Calculate the delta of 12 month CALL with S0=100, while varying strike X from 80 to 120

2e. graph 2a and 2b in the same chart. y-axis is the delta and x-axis is the strike price.

2e. graph 2c and 2d in the same chart. y-axis is the delta and x-axis is the strike price.

3a. Calculate the gamma of 3 month PUT with S0=100, while varying X from 80 to 120

3b. Calculate the gamma of 12 month PUT with S0=100, while varying X from 80 to 120

3c. Calculate the gamma of 3 month CALL with S0=100, while varying X from 80 to 120

3d. Calculate the gamma of 12 month CALL with S0=100, while varying S0 from 80 to 120

3e. graph 3a and 3b in the same chart. y-axis is the gamma and x-axis is the strike price.

3e. graph 3c and 3d in the same chart. y-axis is the gamma and x-axis is the strike price.