 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2010/b/4/d/solution

Use

q = 1/2

and discount one step by

R = 1.1

. At the up node,

A_{1} = 110

and immediate exercise pays

5

. Continuation is worth

(0 + 5/3) / (2 R) = 25/33 < 5

. At the down node,

A_{1} = 100

and immediate exercise pays

15

, while continuation is

(25/3 + 15) / (2 R) = 350/33 < 15

. Thus the American put option should be exercised at either time-one node, and

V_{1} = {5, 15, S_{1} = 120, S_{1} = 100.

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