1. A stock has current price $145. The time to expiration of an option is two years. The stock price volatility is 25%. The annual continuously-compounded risk-free rate is 7.5%. The stock pays no dividends. The price is calculated using two-step binomial model (forward tree) where each step is 1 year in length.
   1. Price the up-and-in call option with barrier $180 and strike price $150.
   2. Price the look-back call option with floating strike.
   3. Price the Asset-or-nothing call option with strike price $150 (owner receives 10 share of stocks if in-the-money)

calculate the call option in each cas