2. Assume that after you estimate the risk neutral model for the continuously com- pounded rate rij you arrive at the following tree: 0 1 2 0 5% 6% 9% 1 CIO 2 4% 5% 1% There is an equal probability of moving up or down on the tree. The time period is one year (A = 1). (a) From a practical perspective, what is the difference between a physical and a risk neutral probability? [5 marks] (b) Calculate the current term structure of annually compounded yields for matu- rities one to three years, i.e., ri(0,T) for T = {1,2,3}. [6 marks] (c) Price a security that has 3 years to maturity and that pays $1 at the end of year 1, 2 and 3, respectively, if the one-year interest rate (annually compounded) at the beginning of the year is less than 5%. That means, at the end of every year, the security will either pay $0 or $1, depending on the interest rate observed at the beginning of the year. Note that the steps i are measuring the beginning of the year, i.e., time 0 denotes today, the beginning of year 1 and 5% at node (0.0) is the annualised continuously compounded interest rate for year 1, measured from step i=0 to step i = 1. [6 marks]