Toronto Skaters' stock is now worth $100.In one month, it will either be $80 or $120.Given that the monthly risk-free rate is 2%, what is the corresponding value of the call? (Assume a strike price $105)

Question

Quizplus · Accepted Answer

We can use the risk-neutral valuation method to calculate the value of the call option.

First, we calculate the risk-neutral probabilities of the stock being worth $80 or $120 in one month using the risk-free rate:

p(down) = (1 + r - u)/(u - d) = (1 + 0.02 - 0.8)/(1.2 - 0.8) = 0.4/0.4 = 1
p(up) = (1 + r - d)/(u - d) = (1 + 0.02 - 0.2)/(1.2 - 0.8) = 0.82/0.4 = 2.05

Next, we calculate the expected value of the stock in one month under the risk-neutral probability measure:

E(S) = p(up) * $120 + p(down) * $80 = 2.05 * $120 + 1 * $80 = $280

Then, we discount the expected stock price back to the present using the risk-free rate:

V(0) = (1 + r)^(-1) * [p(up) * max(S(1) - K, 0) + p(down) * max(S(2) - K, 0)]
where K is the strike price of $105

V(0) = (1 + 0.02)^(-1) * [2.05 * max($120 - $105, 0) + 1 * max($80 - $105, 0)]
V(0) = $10.78

Therefore, the corresponding value of the call option is $10.78. The best choice is C.

Toronto Skaters' Stock Is Now Worth $100