FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 50. Over one period it will either rise to 60 or fall to 40. A European call option with a strike price of 50 expires at the end of the period. What is the call's delta at the initial node, i.e. the number of shares in the replicating portfolio?
The delta is 0.50. In a one-step tree, delta equals the difference in option payoffs (10 minus 0) divided by the difference in stock prices (60 minus 40). That gives half a share, which is the hedge ratio for replicating the call.
- A0.50Correct
- B0.20
- C0.25
- D0.80
Explanation
Call payoffs are 10 in the up state and 0 in the down state. Delta = (10 - 0)/(60 - 40) = 0.50. Dividing the payoff by the initial price gives 0.20, which is the wrong denominator because delta divides by the spread in stock prices.
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