Assignment for October 15

 

7. For the model with W = {w 1,w 2,w 3}, N = 2 risky assets, and r = 0, suppose S1(0) = 6 and S2(0) = 5, and the time 1 prices S(1) = S*(1) are given by

 

asset

w 1

w 2

w 3

1

3

7

7

2

4

4

8

 

  1. Find the risk neutral probability measure.
  2. Find the replicating portfolio for the claim which pays $1 if S2(1)>S1(1), i.e., the claim is worth 1 at w 1 and w 3, and is worth 0 at w 3.
  3. Price this claim in two ways: first, by pricing the replicating portfolio at time 1, and second, using the risk neutra1 probability (compute the expectation of the claim using the risk neutral probability).

 

 

8. The model with W = {w 1,w 2,w 3}, N = 1 risky asset, and r = 0, with S(0) = 5 and time 1 prices given by

 

asset

w 1

w 2

w 3

1

4

5

8

 

admits more than one risk neutral probability measure (and therefore not all contingent claims are attainable).

 

  1. Find two distinct risk neutral probability measures. (Extra credit: describe the set of all risk neutral probability measures)
  2. Find a claim which is not attainable.

 

 

9. Carefully read the "Worked Example" which starts on page 23 of the text, and then do exercise #2.2 on page 27.