• Payoff: the gross outcome of an investment or trade. The amount you earned from that trade, regardless of commissions, extraneous costs, etc.
  • Profits: the gross outcome of an investment or trade, including commissions, extraneous cost
    • → the distinction happens in Options (Finance). Payoffs don’t consider the option premium, while the profits do.
  • Return: short for “rate of return”. The percentage of profit (not payoff!) per original investment. Quoted in percentage (%) or log-returns.

Risk-Neutral Assumption

A risk-neutral world is where there is no risk premium on return. This implies:

No Arbitrage Condition (=Law of One Price)

No arbitrage condition means without any risk, there cannot be excess return (=return above risk-free rate).

Law of One Price states that:

  1. let security have payoff , cost and payoff , cost .
  2. If then