Black-Scholes model shares common intuitions with risk-neutral option pricing model( also known as the binomial option pricing model. One of the biggest underlying assumptions of risk-neutral (binomial)model is that we live in a risk-neutral world. In a risk-neutral assumption is counterfactual,it is brilliant and desirable because the prices of an option estimated by risk-neutral approach are exactly the same with or without the risk-neutral assumptions. Why is that the case, and how is risk -neutral assumption greatly simplifies the calculations of risk-neutral option pricing approach?