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).

What are the call option values (C_u & C_d) across the two states?

Cu= max ( 0, 1.5 x 100 - 120) = $30

Cd= max ( 0, -40) = 0

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

Hedge ratio = 30 / (150 - 80) = 30/70 = 0.428571

What is the probability (Pr_u) that the underlying stock price will experience the 'u' state?

20 = (p*30 + 0)e^-0.055

Therefore p =21.13081 / 30 =0.70436

Value the call using the risk-free approach.

p(0.7)100 + 80 = 100*e^0.055 = 0.366487

C = 30 * 0.366487 *e^-0.055=$11.62

Did I do my math correctly