Suppose the interest rate is fixed at 1% per month. A particular stock follows the price movement below:

a) What is the price of a European put option with maturity two months, and strike of $26? To answer, construct and solve the replicating portfolio problem with position a in shares and b in bonds.

(b) What is the price of an American put option with maturity two months, and strike of $26? Again, construct and solve the replicating portfolio problem with position a in shares and b in bonds. Comment on the difference between the value of the two options, and its decomposition.

Figure 2: Stock Price Movement