Skip to content

FRM Part I · FRM Exam Part I · Binomial Trees

A two-step tree has S0 = 100, u = 1.1 and d = 0.9. The risk-neutral up probability is 0.6 and the per-step discount factor is 0.96. Using backward induction, what is the value of an American put with a strike of 110?

The American put is worth about 10.11. Early exercise is optimal at the down node, where intrinsic value 20 exceeds continuation 17.47. Rolling back, the root continuation value is 10.11, which beats immediate exercise at 10, so the root value is 10.11.

  1. A9.14
  2. B10.00
  3. C10.11Correct
  4. D10.53

Explanation

Terminal stock prices are 121, 99 and 81, giving put payoffs of 0, 11 and 29. At the up node (110): continuation is 0.96 x (0.4 x 11) = 4.224, and intrinsic is 0, so the value is 4.224. At the down node (90): continuation is 0.96 x (0.6 x 11 + 0.4 x 29) = 17.472, below intrinsic 20, so exercise gives 20. At the root: continuation is 0.96 x (0.6 x 4.224 + 0.4 x 20) = 10.11, above intrinsic 10. The European value of 9.14 ignores early exercise at the down node.

Did you get it right without looking?

One question tells you little. A timed set on Binomial Trees shows your real accuracy, how long you take and where you lose marks.

Practise Binomial TreesFree diagnostic mock

More Binomial Trees questions