Question

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 10%. What, to the nearest cent, is the value of a 6-month European call option on the stock with a strike price of $33?

Answer 1

Upmove (U)= High price/current price=36/30=1.2

Down move (D)= Low price/current price=26/30=0.8667

Risk neutral probability for up move

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

=(e^(0.1*0.5)-0.8667)/(1.2-0.8667)=0.55381

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(36-33,0)

=Max(3,0)

=3

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(26-33,0)

=Max(-7,0)

=0

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

=e^(-0.1*0.5)*(0.553813*3+(1-0.553813)*0)

=1.58