Problem 1) Suppose you own a large forest that is due for harvest. The pulp market is picking up, so you know that if you start harvest this year you will forgo rising prices in the future. There is, however, a cost advantage to starting the harvest as soon as possible. The table below shows the present value of the revenue stream and the harvest cost, as functions of the time of harvest. For instance, if you start harvest straight away your revenue stream contribute 10M to your wealth but the costs take 5M away. If you delay harvest till next year, the revenues add 15M to the next year's wealth, and the costs take 6M away, etc. The discount rate is 5%. Use the data below to determine the optimal time to harvest?
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
PV(Revenue) 10 15 20 23 24 23
PV(Costs) 5 6 7 8 8 8
Problem 2)
a) What are the terminal (time 2) payoffs of the options?
b) Derive the risk neutral probabilities for the movement of the binomial tree.Use these to price the call option.
c) would you construct the portfolio of the stock, the call and the risk free asset to exactly replicate the terminal payoffs of the put option?
d) Use the relationship you derived in part c to find the price of the put option.
Problem 3) Decompose the risk of each asset into systematic (market) and idiosyncratic (firm specific risk).
Attachment:- Optimal time to harvest.rar