FRM Part I · FRM Exam Part I · Binomial Trees
In a one-period binomial tree, a stock priced at 100 can move up to 120 or down to 80. A European call option with strike 100 expires at the end of the period. What is the call's delta (the number of shares in the replicating portfolio)?
The call's delta is 0.50. Delta in a binomial tree is the option payoff difference divided by the stock price difference: (20 - 0)/(120 - 80). Half a share replicates the option's exposure to the stock's movement over the single period.
- A0.25
- B0.50Correct
- C0.75
- D1.00
Explanation
Delta = (Cu - Cd)/(Su - Sd). Cu = 120 - 100 = 20 and Cd = 0. Delta = 20/(120 - 80) = 0.50. Using 20/100 = 0.20 or similar ratios ignores the spread between the terminal stock prices.
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