FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at USD 100. In one year it will be either USD 120 or USD 80. The continuously compounded risk-free rate is 5%. Using risk-neutral valuation, what is the risk-neutral probability of the up move (to the nearest 0.001)?
The risk-neutral up probability is 0.628. It equals (e^0.05 minus 0.8) divided by (1.2 minus 0.8), which is 0.251271 divided by 0.4.
- A0.500
- B0.564Correct
- C0.628
- D0.436
Explanation
u = 1.2, d = 0.8. p = (e^0.05 - d)/(u - d) = (1.051271 - 0.8)/0.4 = 0.6282. Wait: 0.251271/0.4 = 0.628. So the correct value is 0.628, not 0.564.
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