Black-Scholes model shares common intuitions with risk-neutral option pricing model (also known as the binomial option pricing model).

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 world, all investors only demand a risk-free return on all assets. Although the risk-neutral assumption is counterfactual, it is brilliant and desirable because the risk-neutral assumption doesn't affect the prices of an option. In another words, prices of an option are exactly the same with or without the risk-neutral assumption. Explain why that is the case, and how risk-neutral assumption greatly simplifies the calculations of risk-neutral option pricing approach.