PLEASE WRITE ALL THE FORMULAS AND CALCULATIONS

Question 1 [24 points]

Consider an economy with two dates (t=0,1) and three states at t=1. The following three assets are traded:

Asset A has a payoff of xA=(2,0,0) Asset B has a payoff of xB=(1,3,0) Asset C has a payoff of xC=(2,2,4)

at t=1. In other words, asset B pays off $1 in state 1, $3 in state 2, and $0 in state 3 at t=1.

1. (b) A put option on asset C with exercise price E=3 is traded. What is the price of this

   option at t=0? [3p]

2. (c) Design a portfolio with payoff (0,0,2) at t=1. What is the price of this portfolio at t=0?

   [4p]

Now consider an (equivalent) economy with three save bonds and four dates (t=0,1,2,3).

Payoff Price t=1 t=2 t=3 t=0

Bond A 2 0 0 1.80 Bond B 1 3 0 3.30 Bond C 2 2 4 6.20

In other words, e.g. bond B costs $3.20 at t=0 and pays off $1 at t=1, $3 at t=2, and $0 at t=3.

4. (d) What is the definition of a yield curve (or term structure of interests)? [2p]

5. (e) Determine the yield curve in this economy. [6p]

6. (f) If there is no arbitrage, the yield curve is always flat. Is this statement true? [3p]