The range of S is 74 while that of P is 37 across the two states. What is the hedge ratio of the put

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

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