Question

One Period Binomial Model, Using the AAPL option chain, solve for the at the money (X = 225) call and put options. Assume U = 1.2, πu= 0.6, Rf = 0.50%. Show all your work.

Answer 1

Since it is an at the money 1-period option, the current stock price is equal to the strike price at the end of 1st period. So stock price = S = 225

Strike price = X = 225

Upmove factor = U = 1.2

So, Downmove factor = D = 1/U = 0.8333

Probability of upmove = P_U = 0.6

So, Probability of upmove = P_D = 1 - 0.6 = 0.4

Rf = 0.5%

Stock price after upmove = S⁺ = 225 x 1.2 = 270

Stock price after downmove = S^- = 225 x 0.8333 = 187.50

Calculating the payouts in case of Call option

Upmove Payout⁺ = Maximum of $0 and ($270 - $225) = $45

Downmove Payout⁺ = Maximum of $0 and ($187.50 - $225) = $0

So Call Option value = (P_U x Upmove Payout⁺ + P_D x Downmove Payout⁺) / (1 + Rf) = (0.6 x $45 + 0.4 x $0) / (1.005) = $26.87

Calculating the payouts in case of Put option

Upmove Payout⁺ = Maximum of $0 and ($225 - $270) = $0

Downmove Payout⁺ = Maximum of $0 and ($225 - $187.50) = $37.50

So Put Option value = (P_U x Upmove Payout⁺ + P_D x Downmove Payout⁺) / (1 + Rf) = (0.6 x $0 + 0.4 x $37.50) / (1.005) = $14.93