Definition (Derivative)

A derivative is a process $(O_{t})_{t\in[0,1]}$ adapted to the filtration $(\mathcal{F}_{t})_{t\ge 0}$ of the market model.

Definition (Maturity)

We call $T$ the expiration or maturity time of the derivative.

Definition (Payoff)

$O_{T}$ is called the payoff of the derivative at expiration.

Definition (Forward contract)

A Forward Contract is a derivative with payoff $$O_{T}=S_{T}-K$$