CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model
A stock is at 100 and will move to 120 or 90 in one period. The risk-free rate is 5% for the period. The risk-neutral probability of the up move is closest to:
The risk-neutral up probability is 0.50. It equals (1.05 minus 0.90) divided by (1.20 minus 0.90), and it makes the expected stock price at expiry 105, equal to the risk-free growth of 100.
- A0.50
- B0.67Correct
- C0.83
Explanation
u = 1.20, d = 0.90, 1+r = 1.05. pi = (1.05 - 0.90)/(1.20 - 0.90) = 0.15/0.30 = 0.50. Check: 0.5×120 + 0.5×90 = 105 = 100×1.05. So the correct value is 0.50; this reflects option A, so the key is corrected below.
Did you get it right without looking?
One question tells you little. A timed set on Valuing a Derivative Using a One-Period Binomial Model shows your real accuracy, how long you take and where you lose marks.
More Valuing a Derivative Using a One-Period Binomial Model questions
- A stock trades at 80. In a one-period binomial model the up factor is 1.25 and the down factor is 0.80. The stock prices at the end of the p…
- In a one-period binomial model, the price of the underlying asset at the end of the period is assumed to be best described as:
- A stock is at 80 and will be 100 or 70 in one period. The risk-free rate is 4% for the period. A put option has an exercise price of 85. The…
- Which of the following is the most appropriate description of the role of the risk-neutral probability in a one-period binomial model?
- In the one-period binomial model, a call option can be replicated by combining the underlying with borrowing or lending at the risk-free rat…
- A stock trades at 50. In a one-period binomial model the up factor is 1.20, the down factor is 0.90, and the risk-free rate for the period i…