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FRM Part I · FRM Exam Part I · Binomial Trees

A stock trades at 50. Over one year it moves up by a factor of 1.2 or down by a factor of 0.8 in a single-step tree. The continuously compounded risk-free rate is 5%. Using the risk-neutral probability of an up move (about 0.6282), what is the value of a one-year American put with a strike of 60?

The American put is worth 10.00. The continuation (European) value is about 7.07, which is below the immediate exercise value of 60 minus 50, which is 10. Because intrinsic value exceeds continuation value, early exercise is optimal and the option takes the higher value.

  1. A7.07
  2. B10.00Correct
  3. C11.95
  4. D20.00

Explanation

At the up node the stock is 60 and the put pays 0. At the down node the stock is 40 and the put pays 20. The continuation value is e^-0.05 x 0.3718 x 20 = 7.07. Immediate exercise at the root gives 60 - 50 = 10, which is higher, so the American put is worth 10.00. The 7.07 option is the European value, which ignores early exercise.

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