We obtained the binomial option pricing formula by hedging a short position in the call option with a long position in stock. An alternative way to do this is to combine the stock and a risk-free bond to replicate the call option.

Construct a one-period binomial option pricing model in which the stock and a risk-free bond are used to replicate a European call option. Then show that the option pricing formula is the same as the one developed in the text.

Hint: Hold ns shares of stock and issue B dollars of bonds paying r percent so that the value in both outcomes matches precisely the value of the option.

Then solve for ns and B and substitute back into the formula for the value of the hedge portfolio today to obtain the formula for C.