St. Johns Inc. stock is currently selling for $25 and has a volatility of 25%. The 7-month risk-free rate is 3% with continuous compounding. Use a 7-step binomial tree to answer these questions.
a. Price a 7-month up-and-out call option with a strike of $26 and a barrier of $33
b. Price a 7-month up-and-in call option with a strike of $26 and a barrier of $33
c. Price a 7-month vanilla call option with a strike of $26
d. What is the relationship to the price of the three options?