The current price of TechSIM Co. stock is $100. Below is a blank binomial lattice that you can use to show the possible price paths of TechSIM Co. stock over the nexttwo6-month periods and to calculate option values. The up and down factors have been calculated to match the volatility of TechSIM Co. stock. If the price rises, it rises by 30% (to 1.3 times its prior value); if it falls, it falls by 23% (to .77 times its prior value). The effective 6-month risk-free rate is .005 (.5%). (SHOW THE TREES)

t = 0t = 1t = 2

S₀= 100

Note: t is measured in 6-month periods.

A. What is thet = 0value of anAmerican put optionwritten on TechSIM Co. stock with a strike price of $105? Show you work on the next page if necessary. You may write on the tree diagram above. (10 points)

Put Value = ________________

B. What is the initial portfolio at t = 0 that allows someone to replicate the payoffs on the above put option? Show your work on the next page. You can buy or sell fractions of shares. (5 points)

X (i.e., the number of shares of the underlying; X < 0 is a short position) = ___________________

B (the amount borrowed (B<0) or lent (B>0) at the risk-free rate) = ______________________