Question

1. (5 points) Find the value of a call option using a one-period binomial lattice model. The underlying stock has initial price $100 and lattice parameters u = 5/4, d = 4/5. The risk free interest rate is 10% and the strike price is $105.

Answer 1

High price=Current price*up move=100*1.25=125

Low price=Current price*down move=100*0.8=80

Risk neutral probability for up move

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

=(e^(0.1*1)-0.8)/(1.25-0.8)=0.67816

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(125-105,0)

=Max(20,0)

=20

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(80-105,0)

=Max(-25,0)

=0

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

=e^(-0.1*1)*(0.678158*20+(1-0.678158)*0)

=12.27