FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 50 and in one period will move to 60 or 40. A European put with strike 48 expires at the end of the period. What is the put's delta from the one-step binomial tree?
The put's delta is -0.40. The put pays 0 in the up state and 8 in the down state, so delta is (0 - 8)/(60 - 40). The negative sign shows the put gains when the stock falls, offsetting a long stock position.
- A-0.40Correct
- B+0.40
- C-0.60
- D-0.80
Explanation
Put payoffs: Pu = max(48-60,0) = 0 and Pd = 48-40 = 8. Delta = (0 - 8)/(60 - 40) = -0.40. The call on the same tree has delta 12/20 = 0.60, and put delta equals call delta minus 1, which is -0.40. The -0.60 option mistakenly flips the sign of the call delta.
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