Why Risk-Neutral Pricing Cannot Independently Value Stocks or Bonds

Summary

The document asks whether a stock or bond can be valued by forecasting future cash flows and discounting them at the risk-free rate. Its answer explains risk-neutral valuation through replication: a derivative can be priced when its payoff can be reproduced using traded instruments, because arbitrage links the derivative’s price to the replicating portfolio.

Stocks and bonds are treated here as basic instruments that cannot be independently replicated from other assets for this purpose. Risk-neutral probabilities can still describe the relationship between a current price and discounted expected future prices, but they do not supply an independent price when the probabilities themselves depend on the price being found. The response is a short conceptual explanation rather than a full treatment of asset pricing. It does not discuss practical valuation models, credit risk, dividends, or the assumptions needed to construct risk-neutral measures in particular markets.

Key ideas

• Risk-neutral valuation relies on replication using traded instruments.
• A replicable payoff can be priced by matching it to the cost of its replicating portfolio.
• The answer argues that a stock or bond cannot generally be priced independently this way as a basic asset.
• Risk-neutral expectations describe a price relationship but do not by themselves determine the price when the measure depends on that price.

Tags

# Can we use risk-neutral pricing to price a stock or a bond?


# Can we use risk-neutral pricing to price a stock or a bond?












Can you please tell me whether if I can used risk-neutral pricing approach to price a stock or a bond ? (i.e. discount with risk free rate the future cashflows) ?

Thank you very much!

## Answer by Arshdeep (score 4)

https://quant.stackexchange.com/a/54947

In essence, risk neutral pricing is based on the idea of 'replication' - the instrument that is being valued can be created artificially by other instruments already available. It is kind of like saying that if I can make an orange from 2 apples and 3 mangoes, then price of an orange better by twice the apple price added to thrice the mango price.

As bonds/stocks are basic instruments you can't really replicate, you cannot use risk neutral pricing to value these. Note that they will still obey the expectations with the risk neutral probabilities (i.e. price of the stock today will be discounted average of stock price possibilities tomorrow, over the risk neutral probabilities; but you can't really use this to price the stock itself, since you need the stock price to find these probabilities).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.