FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at USD 50. Over the next year it will either rise to USD 60 or fall to USD 40. A one-year European call has a strike of USD 50. The continuously compounded risk-free rate is zero for simplicity. What is the number of shares in the replicating (delta-hedge) portfolio for one long call?
The replicating portfolio holds 0.50 shares. Delta equals the call payoff difference (10 minus 0) divided by the terminal stock price difference (60 minus 40), which gives 0.50.
- A0.25
- B0.50Correct
- C0.75
- D1.00
Explanation
Call payoffs: up = 10, down = 0. Delta = (10 - 0)/(60 - 40) = 0.50. A wrong approach is dividing by the current price spread (50), giving 0.20 or other values; the correct denominator is the difference between terminal stock prices.
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