Question

The current price of Estelle Corporation stock is $25. Its stock price will either go up by 20% or go down by 20% in one year. The stock pays no dividends. The one-year risk-free interest rate is 6%. Using the binomial model, calculate the price of a one-year call option on Estelle stock with a strike price of $25. The price of a one-year call option on Estelle stock with a strike price of $25 is $ (Round to the nearest cent.)

Answer 1

Upmove (U)= High price/current price=30/25=1.2

Down move (D)= Low price/current price=20/25=0.8

Risk neutral probability for up move

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

=(e^(0.06*1)-0.8)/(1.2-0.8)=0.65459

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(30-25,0)

=Max(5,0)

=5

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(20-25,0)

=Max(-5,0)

=0

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

=e^(-0.06*1)*(0.654591*5+(1-0.654591)*0)

=3.08