A stock with a current price of $22 will either move up to $32.00 or down to $15 over the next period. The risk-free rate of interest is 1.1%. What is the value of a call option with a strike price of $25?
A)$2.20
B)$2.34
C)$2.67
D)$2.79
E)$2.41

Question

Quizplus · Accepted Answer

To value the call option, we can use the binomial option pricing model. First, calculate the up and down factors (u and d), and then the risk-neutral probabilities (p and 1-p).Given:- Current stock price (S) = $22- Upward price (Su) = $32- Downward price (Sd) = $15- Risk-free rate (r) = 1.1% or 0.011- Strike price (K) = $251. Calculate the call option payoff in the up and down states:   - Upward payoff = max(Su - K, 0) = max(32 - 25, 0) = $7   - Downward payoff = max(Sd - K, 0) = max(15 - 25, 0) = $02. Calculate the risk-neutral probability (p):   - p = (e^(rΔt) - d) / (u - d)   - Assuming Δt = 1 (one period), and since e^(0.011) ≈ 1.011, u = 32/22, and d = 15/22,   - p ≈ (1.011 - 15/22) / (32/22 - 15/22) ≈ 0.5113. Calculate the expected payoff of the option:   - Expected payoff = e^(-rΔt) * (p * Upward payoff + (1-p) * Downward payoff)   - ≈ 1/1.011 * (0.511 * 7 + (1-0.511) * 0) ≈ $2.41Therefore, the value of the call option is approximately $2.41, which corresponds to choice E.

A Stock with a Current Price of $22 Will Either