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

  • All Present Value Calculations are done at the risk-free rate
  • All assets have risk-free rate of return (=zero riNo-Arbitrageitrage Condition]] holds
  • & This is not really realistic, but simplifies calculations a lot.

Risk-Neutral Measure

A risk-neutral measure is a probability measure such that , in other words, all securities have risk-free rate of return.