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Could you please explain why to calculate the asset price under risk-neutral probability, we have to take the expectation of the future cashflow, while in the normal world, we don't have to take the expectation of future cashflow ? (i.e. we keep the same amount of future cashflow then discounted for its required rate of return)

Thank you very much.

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while in the normal world, we don't have to take the expectation of future cashflow

Grossly incorrect. The formula or approach are exactly the same: the value of an asset is the expectation of its discounted cash flow. The only difference is the discount rate. If you have a nonlinear instrument such as a vanilla Euro call option, it's not clear what should be the discount factor in real world. The discount factor should include the risk premium, so what is the risk premium of this option?

That's where the risk neutral trick comes handy. It turns out that you can form a portfolio of the derivative instrument and some other instruments with known values (such as underlying stocks) in such a way that the cash flow of this portfolio is fixed. If it is fixed then there is no uncertainty, there is no risk. Hence, there is no need to think of the risk premium. Therefore, you can discount at risk free rate. Then you remove the value of known assets, and the remaining is the value of the derivative.

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