CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
A stock trades at 100. After one period it will be either 120 or 80. 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 0.625. It is (1.05 − 0.80)/(1.20 − 0.80). This probability makes the expected stock value equal 105, which is today's price grown at the risk-free rate, so 0.50 is wrong.
- A0.50
- B0.625Correct
- C0.75
Explanation
Up factor u=1.20, down factor d=0.80, 1+r=1.05. pi=(1.05-0.80)/(1.20-0.80)=0.25/0.40=0.625. Check: 0.625*120+0.375*80=75+30=105=100*1.05. Using 0.50 ignores the risk-free growth.
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