TreeOlivia's stock price is $180 and could halve or double in each six-month period. The interest rate is 12% a year. What is the value of a six-month call option on TreeOlivia with an exercise price...

TreeOlivia's stock price is $180 and could halve or double in each six-month period. The interest rate is 12% a year.

1. 
   

   What is the value of a six-month call option on TreeOlivia with an exercise price of $120?

   
   


2. 
   

   What is the option delta for the six-month call with an exercise of $120?

   
   


3. 
   

   The payoffs of the six-month call option can be replicated by buying shares of stock

   
   

   and borrowing. What amount should be invested in stock and what amount must be

   
   

   borrowed? Assume the exercise price is $120.

   
   


4. 
   

   What is the value of the one-year call option on TreeOlivia with an exercise of

   
   

   $150? (Hint: use the two-step binominal tree)

   
   


5. 
   

   What is the value of the one-year put option on TreeOlivia with an exercise of $150?