Risk-Neutral Assumption

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 $\mathbb{E}(S_0)=e^{rt}$, in other words, all securities have risk-free rate of return.