I am struggling with this concept of risk neutral probabilities. My understanding of how a risk neutral pricing framework works is as follows: (discrete, binomial lattice for simplicity) I do not know the actual or real world probability "P" of Upstate of say a risky bond. Say the price in the market (assuming it is correctly priced) is S1 and the risk free rate is 5%. Now i assume a world where the investors are risk averse, I calibrate my model to find "Q". And using Q i get my model price to equal the market price. The bond was risky, but i'd still use Rf (5%) as the discount rate.
Why is risk-free rate the appropriate discount rate? I just inculcated the risk, should it not be the risk free rate plus risk premium? Is it only because this hypothetical world's risk neutral assumption forces us to use Rf? How exactly did we take the risk out of equation? I think we added it to the mix.
As an aside, I'd be happy to hear your layman explanation of what we are trying to do under risk neutral valuation.
