In a 2-period Binomial option pricing model (BOPM) the up and down moves in the stock price are U=1.1 and D=0.8, the current stock price is S₀ =100 and the risk-free rate is r=2% per period (simple rate). The strike price is K = 100 and T=maturity date of the option.

A down-and-out put option has a payoff = max (K S_T , 0 ), unless the stock price falls below a lower barrier L=82 , in which case the payoff is zero.

A down-and-in put option has a payoff = max (K S_T , 0 ) but only if the stock price falls below L=82.

Using the two-period BOPM what is the price of

a). plain vanilla put option (K=100).

b). down-and-out put option (K=100).

c). down-and-in put option (K=100).

Briefly comment on any intuition behind the above results.

To aid your exposition, fill in the entries in the table below (for each option considered).

Path Number Path Probability S(O) $(1) $(12) Payoff Expected Payoff uy ud HnM+ 100 100 100 100 Path Number Path Probability S(O) $(1) $(12) Payoff Expected Payoff uy ud HnM+ 100 100 100 100