FRM Part I · FRM Exam Part I · Binomial Trees
A stock starts at 100 and in each of two periods moves up by a factor of 1.2 or down by a factor of 0.8. The risk-free rate is 5% per period (simple discounting), so the risk-neutral up probability is 0.625. An American put has strike 105 and two periods to expiry. What is its value today?
The American put is worth 10.84. Working backward, the up node is worth 3.21 and the down node is exercised early for 25, since its holding value is only 20. Discounting the risk-neutral expectation of those values gives 10.84, which exceeds immediate exercise of 5.
- A9.06
- B11.38
- C5.00
- D10.84Correct
Explanation
Terminal prices are 144, 96 and 64, with put payoffs 0, 9 and 41. Up node (120): hold = 0.375×9/1.05 = 3.21; intrinsic is 0, so 3.21. Down node (80): hold = (0.625×9 + 0.375×41)/1.05 = 20.00, but intrinsic is 25, so exercise and value 25. Root: hold = (0.625×3.214 + 0.375×25)/1.05 = 11.384/1.05 = 10.84, which is above intrinsic 5. The 9.06 option is the European value, which ignores early exercise at the down node.
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