FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at 100. In a two-step tree each step has u = 1.10, d = 0.90 and a risk-free rate of 5% per step, so p = 0.75. For a European call with strike 100 and two steps to expiry, what is the initial hedge ratio (delta) at the root, using the values at the first-step nodes?
Delta at the root is 0.75. The call is worth 15 at the up node (110) and 0 at the down node (90). Delta is the change in option value over the change in stock price, (15 - 0)/(110 - 90) = 0.75.
- A0.525
- B0.75Correct
- C0.136
- D0.5625
Explanation
At the up node (S = 110) the call is worth (0.75×21 + 0.25×0)/1.05 = 15. At the down node (S = 90) both successors (99 and 81) are below the strike, so the call is worth 0. Delta = (15 - 0)/(110 - 90) = 0.75. Dividing 21 by 40 uses terminal nodes, which is the wrong spacing for the first-step delta.
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