Question

Currently, a call option on Bayou stock is available with an exercise price of $100 and an expiration date one year from now. Assume that the price of Bayou Corporation stock today is $100. Furthermore, it is estimated that Bayou stock will be selling for either $62 or $152 in one year. Also, assume that the annual risk-free interest rate on a one-year Treasury bill is 10 percent, continuously compounded. Therefore, the T-bill will pay $100 × e^(0.1), or $110.25.

Find the call option premium using the Binomial model.

Answer 1

So = current stock price = 100$

Sou = Stock price if price moves up = $152

Sod = Stock Price if price moves down = $62

u = Sou/So

=152/100

=1.52

d = Sod/So

= 62/100

= 0.62

probability = p = e^rt - d/u-d

=e^10% - 0.62 / 1.52-0.62

=1.1025-0.62 / 1.52-0.62

= 0.4825/0.90

= 53.61%

Thus price of call option = [Fu(p) + Fd(1-p)] / (1+r)^n

=[52(53.61%) + 0(1-53.33%)] / (1+10%)^1

= 27.8772 / 1.1

= $ 25.34