A risk-neutral decision maker carries a stock option for one day. This option pays him $(P — 50) is the stock price, P, is above 50 and pays him 0 otherwise. The current stock price is $45, and each...

A risk-neutral decision maker carries a stock option for one day. This option pays him $(P — 50) is the stock price, P, is above 50 and pays him 0 otherwise. The current stock price is $45, and each day it can go up 20% or down 20% with probabilities 0.6 and 0.4, respectively. What is the value of this option for one day? Repeat if the decision maker has a three-day option on this stock, and he can

• Exercise this option only on the third day, or

• Exercise this option at any day during the three days.