Mateusz: ignore this post, it's a very techincal point to Mark that is beyond SP2 (I don;t even think it's covered in SP6).

Mark: I don;t believe that a replicating portfolio is required for risk-neutral pricing. Risk-neutral pricing requires the absence of arbitrage*.

The first fundamental theorem of asset pricing states: A market** is arbitrage free if and only if there exsits an equivalent martignale measure.

The second fundamental theorem of asset pricing states: The equivalent martingale measure is unique if and only if the market is complete.

https://en.wikipedia.org/wiki/Fundamental_theorem_of_asset_pricing
Therefore, if we assume the market is arbitrage free, we can can use risk neutral pricing. The question then becomes what is the risk-neutral measure (RNM)/market price of risk.

1. If the market is complete, the RNM is unique and the maths tell you it.

2.It the market is not complete, the RNM is not unique. If there is a deep and liquid market, we can infer the market price of risk/RNM from market prices.

3. If there isn;t a deep and liquid market, then you use expert judgement to decide the market price of risk and hence the RNM.

*this is true in a discrete model. For a continuos model we require a similar concept called "no free lunch with vanishing risk"

** with discrete prices!

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