FRM Part I · FRM Exam Part I · Binomial Trees
A futures price is 100. In a one-year, one-step tree it moves to 120 or 90. The risk-free rate is 6% continuously compounded. What is the value of a one-year European put option on the futures with strike 105?
The put is worth about 9.42. Because futures prices have zero risk-neutral drift, the up probability is 1/3 and the down probability is 2/3. The expected payoff is 2/3 x 15 = 10, discounted at 6% for one year.
- A9.42Correct
- B10.00
- C6.51
- D4.71
Explanation
A futures price has zero drift under risk-neutral valuation, so p = (1 - d)/(u - d) = (1 - 0.90)/(1.20 - 0.90) = 1/3. The put pays 0 in the up state and 15 in the down state. Value = e^{-0.06} x (2/3) x 15 = 0.941765 x 10 = 9.42. Using p = (e^{0.06} - d)/(u - d) = 0.5395 would give 6.51, which is wrong for futures.
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