Use the two-state binomial option-pricing model with continuous compounding for the following questions:

• S₀ = $100; X = $120; r_f = 5.5%
• The stock price will either increase to $150 (u=1.5) or decrease to $80 (d=0.8).

1. What is the delta (i.e., hedge ratio) for the put?

2. What is the probability (Pr_u) that the underlying stock price will experience the u state? (Same as above)

3. Value the put using the risk-free approach.

4. Value the put using the risk neutral approach.