Your task is to analyze options on a fund. The time horizon for the analysis is T = 1 ar. The fund has time 0 price S0 = 80 and continuous dividend rate = 0, 02 (pro anno). Use a 4-period binomial model with 'up' and 'down' factors u = 1, 12 and d = 0, 85, respectively. This means that each part-three covers one time period of h = T / 4 = 0, 25 years (3 months). Assume that risk-free, continuous interest rate is r = 0, 02 (pro anno). First, consider a European put option on this fund with an exercise price of K = 80 and time to maturity T = 1. a) Calculate time 0 the price of this option. b) What is the market price of this option at time t = 0, 5 in node out, ie given that the value of the fund has increased by the factor u once and decreased by factor d once in the first 6 months. Consider the replicating portfolio of this option. The replicating portfolio consists of units of the fund and the amount B invested at risk-free interest rate. c) Consider node u at time t = 0, 25, ie the value of the fund has increased after 3 months. Calculate the replicating (outgoing) portfolio ( and B) in this the node. Also calculate the value of this (inbound) portfolio in the following the node out, ie given that the value of the fund decreases in the next period. d) Consider node d at time t = 0, 25, ie the value of the fund has decreased after 3 months. Calculate the replicating (outgoing) portfolio ( and B) in this the node. Also calculate the value of this (inbound) portfolio in the following the node you, ie given that the value of the fund goes up in the next period.

e) Consider node out at time t = 0, 5, ie the value of the fund has both gone up and down the first 6 months. Calculate the replicating (outgoing) portfolio ( and B) in this node. Check that this portfolio can be financed using an inbound portfolio - regardless of whether node ud nas from node u or D in the preceding period.