=+If the writer bought this (hedging) portfolio (, ) at t = 0 and held it, the

=+If the writer bought this (hedging) portfolio (ϕ, ψ) at t = 0 and held it, the equations (7.3) guarantee that he achieves his goal: if the stock moves up then the portfolio becomes worth fb and if the stock moves down the portfolio becomes worth fa

.

Thus, the fair price (premium) the writer should be paid for that option is equal to where ϕ and ψ are from (7.3). Having this amount of money the writer can meet his obligation to the holder if he follows the right strategy. At the same time, charging this premium, he cannot make a risk-free profit. We observe that using the portfolio (ϕ, ψ) we have synthesised3

(replicated) the