Question

The current price of Estelle Corporation stock is $ 30.00. In each of the next two​ years, this stock price will either go up by 23 % or go down by 23 %.The stock pays no dividends. The​ one-year risk-free interest rate is 7.6 % and will remain constant. Using the Binomial​ Model, calculate the price of a​ one-year put option on Estelle stock with a strike price of $ 30.00. The price of the​ one-year put option is ​$_____(Round to the nearest​ cent.)

Answer 1

High price=Current price*up move=30*1.23=36.9

Low price=Current price*down move=30*0.77=23.1

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.076*1)-0.77)/(1.23-0.77)=0.67166

Put option payoff at high price (payoff H)

=Max(Strike price-High price,0)

=Max(30-36.9,0)

=Max(-6.9,0)

=0

Put option payoff at low price (Payoff L)

=Max(Strike price-low price,0)

=Max(30-23.1,0)

=Max(6.9,0)

=6.9

Price of Put option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.076*1)*(0.671658*0+(1-0.671658)*6.9)

=2.1