Ch$21$: You are attempting to value a put option with an exercise price of $$180$ and one year to expiration. The

underlying stock pays no dividends, its current price is $$180,$ and you believe it has a $50\%$ chance of

increasing to $$200$ and a $50\%$ chance of decreasing to $$100.$ The risk$-$free rate of interest is $12\%.$

Required:

a$.$ What will be the payoff to the put, $P_u,$ if the stock goes up$?$

b$.$ What will be the payoff, $P_d,$ if the stock price falls?

c$.$ What is the weighted average value of the pay off?

Answer is complete but not entirely correct.

Complete this question by entering your answers in the tabs below.

What is the weighted average value of the pay off?

Note: Do not round intermediate calculations. Round your answer to $3$ decimal places.