Question

Already answer part a), please help with part b), THANK YOU!

7. (20 pts) Suppose the price of a non-dividend paying stock is $100 today and the continuous compounding interest rate is r = 7%. (7a) (10 pts) Find the range for the price of an American put with strike price X = 110 and expiry time T = 2. (7b) (10 pts) Suppose that the price of an European call with strike price X = 110 and expiry time T = 2 is $6, find the range for the price of an American put with the same strike price X and expiry time T.

Answer 1

stock price = $100

continuous compounding interest rate = 7%

Range for an American put is given by {min value, max value} = {Max(0,(X-St)), X}

Range for an European put is given by {Max(0,(X*e^-rt-St)), X*e^-rt}

Part a:

Range for American put = {Max(0,(X-St)), X} = {Max(0,(110-100)), 110} = {Max(0,(10)), 110} = {10,110}

Part b: We need to determine St from the given information to calculate the range for the American put.

Range Price of European call = (Max(0,(St - X*e^-rt ), St)

Price of European call = St - X*e^-rt = St - 110*e^-7%*2 = St - 95.6294

This is given as $6. hence 6 = St - 95.6294

this gives us the value of St as $101.6294

The range for American put = {Max(0,(X-St)), X}

substituting the value in the range above we will get the range for American put

Range for American put = {Max(0,(X-St)), X} = {Max(0,(110-101.6294)), 110} = {Max(0,(8.3706)), 110}

= {8.3706, 110}

Answer:

The range for the American put is  {8.3706, 110}