A stock price is $100 and can go up or down $10 in one month. The risk-free inte
ID: 2762347 • Letter: A
Question
A stock price is $100 and can go up or down $10 in one month. The risk-free interest rate is 5% and no dividends are scheduled.
a)Using the binomial model calculate the value of a 1-month at-the-money European call.
b)Calculate the implicit probability p of the stock price going up to $110 in one month. HINT: Express the discounted expected call payoff as a function of p, match your answer in (a) and solve for p. c) What is your annualized expected return and risk if you invest in the stock? Is your answer consistent with portfolio theory?
Explanation / Answer
Rf = 5/12
= 0.42%
(B) Implicit probability p of the stock price going up (P) = S*(1+Rf) – D/U-D
= 100*(1.0042)– 90/110-90
= 100.42-90/20
= 0.521
(1-P) = 1-0.521
= 0.479
Stock price =$100
Assuming strike price = 105
Stock upward price = $110 Strike price: $105 Option Price movement = $5
(Option will be exercised)
Stock downward price = $90 Strike price: $105 Option Price movement = 0
(Option will not be exercised)
(A)Value of call option = Expected value after one year / 1.0042
= ($5*0.521) +(0*0.479) / 1.0042
= $2.59
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.