This question is incomplete, the complete question is;
We will derive a two-state put option value in this problem.
Data: S₀ = 106; X = 112; 1 + r = 1.12. The two possibilities for ST are 149 and 75.
The range of S is 74 while that of P is 37 across the two states. What is the hedge ratio of the put
Answer: the hedge ratio of the put H = - 1/2 ≈ - 0.5
Explanation:
Given that;
S₀ = 106, X = 112, 1 + r = 1.12
Us₀ = 149 ⇒ Pu = 0
ds₀ = 75 ⇒ Pd = 37
To find the Hedge ratio using the expression
H = Pu - Pd /Us₀ - ds₀
so we substitute
H = 0 - 37 / 149 - 75
H = - 37/ 74
H = - 1/2 ≈ - 0.5
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