CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
A stock trades at 100 and may rise to 120 or fall to 90 in one period. The risk-free rate is 5% per period. The risk-neutral probability of the up move is closest to:
The risk-neutral up probability is 0.50. It equals (1.05 − 0.90) divided by (1.20 − 0.90), or 0.15/0.30. Under it, the expected stock price of 105 equals the current price of 100 grown at the 5% risk-free rate.
- A0.33
- B0.50Correct
- C0.67
Explanation
Gross up factor 1.20, down 0.90, risk-free 1.05. Probability = (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. The 0.67 figure comes from wrongly using 0.20/0.30 style ratios.
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