108156.pdf

Solutions 275

Figure S.4 Tree of price movements in Exercise 3.2

Figure S.5 Tree of price movements in Exercise 3.3

3.5The return over two time steps as compared to the sum of one-step returns

can take the following values:

Scenario K(0,2) K(1) +K(2)

ω 1 15 .50% 15 .00%

ω 2 15 .50% 15 .00%

ω 3 − 5 .50% − 5 .00%

Over three time steps we have

Scenario K(0,3) K(1) +K(2) +K(3)

ω 1 3 .95% 5 .00%

ω 2 27 .05% 25 .00%

ω 3 3 .95% 5 .00%

The sum of one-step returns tends to be larger then the return over the total

interval if the sign of one-step returns alternates.

3.6First findK(0,2) and then the one-step returnsK(1) =K(2) =Kfrom the