Option Pricing
We are going to find the price of a put and a call options. The underlying assets is the stock S. The price of the stock today is S0=40, the strike price of the option is K=50. The option matures in 4 periods.
Q1) What is the payoff of the call and the put?
Q2) At each period the stock can go up by a factor of "u" or down by a factor of "d". If u=2 and d=1/2. Construct the lattice of all the possible states of the world for the following four periods.
Q3) Calculate the risk neutral weights using u, d, and the risk free rate r=25%.
Q4) Using backward induction and the risk neutral weights solve the price of the call.
Q5) Using backward induction and the risk neutral weights solve the price of the put.
Decision analysis
You want to make a party and charge for it. You can do it outdoors, on a porch, or indoors. You are afraid it may rain. So far you believe that the chances of raining are 60%.
If you do the party outdoors and is sunny you will make $100, but if rains you will get 0$.
If you do the party in the porch and is sunny you will make $90, but if rains you will get 20$.
If you do the party indoors and is sunny you will make $40, but if rains you will get $50.
Q6) Model the problem with a tree diagram.
Q7) Assume the Utility function is U(x)=(4/3)*[1-(1/2)x/50]. What are the utilities of the payoffs?
Q8) What is the expected utility of each alternative?
Q9) What is the value in dollars? (Also called the certain equivalent).
Q10) Which alternative is the best?