How Market Expectations Enter Stock Prices and Risk-Neutral Option Pricing
Summary
The discussion explains why a stock's current price can be treated as incorporating investors' expectations about its future value. If market participants see an attractive risk-adjusted opportunity to buy or sell, their orders can move the price until the expected excess return is reduced. One response frames the price as near expected future value, adjusted for risk aversion and discounting; another illustrates how buying at available ask prices can push the market higher.
This intuition helps explain risk-neutral option pricing: in an actively traded market, the underlying asset's price already reflects market expectations, so option valuation need not separately insert the stock's expected return in the same way. The answers are conceptual rather than a formal derivation. They do not establish that market prices equal expected future prices exactly, and the discussion gives little detail about heterogeneous beliefs, risk premia, or market frictions.
Key ideas
- Trading in response to perceived mispricing can move a stock price toward a level where excess risk-adjusted returns diminish.
- Market prices reflect participants' views as expressed through orders, and those views can change quickly.
- Risk-neutral option pricing treats the underlying price as already embodying market expectations.
- The discussion offers intuition rather than a complete mathematical treatment of risk premia or trading frictions.
Tags
Full text
# Answer by Mark Joshi (score 1) # Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future? I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf On the second page, under the subsection titled "The Risk-Neutral World" it points out that the model previously used to value options contracts does not take into account the probability of prices going up or down. It then suggests that this may be because a stocks current price takes into account the probability of it going up (or down) in the future. Can anyone explain, in simple terms, why this might be true? ## Answer by Mark Joshi (score 1) https://quant.stackexchange.com/a/19290 well, the current share price reflects fair value. So you'd expect it to be close to its expected price, but slightly below because of risk aversion and discounting. If it was very far off its expectation, it would either be over or under valued and people would trade accordingly. ## Answer by Neeraj (score 0) https://quant.stackexchange.com/a/19297 Mark has rightly pointed. You may think like this, If there is high probability price would go up in future(in very short period), lets say 90% then investors would continue to buy until they no longer expect price to increase with such a high probability. Or until this strategy of buying shares with high probability of going up is not profitable(excess risk adjusted return). Similarly, if there is very high probability that price will fall in future, then investors would continue to sell until they no longer expect price to fall beyond that level. Or until this strategy of selling shares with high probability of going down is not profitable(excess risk adjusted return). So your question : is it realistic to assume that current price of stock takes into account probability of going up and down in the future? Answer is completely yes. After all price are not deterministic. Lets come to your dilemma on pricing of option contract. Since derivatives derive their value from some underlying assets it is completely realistic to assume that current price of security is fair( only for actively traded) and hence does not require to take into account expected return on the underlying one. I hope it would help you to understand. ## Answer by Kyle Balkissoon (score 0) https://quant.stackexchange.com/a/19310 What the author is arguing is that the current price exactly at this instant takes into account all the views of the market participants as expressed by orders (which would be correct). Note that those views may change almost instantaneously generating orders thus causing price to change. An example is you have an expected future price of 10 and the current price is 9, therefore you will allocate a certain amount of capital to this trade (say 1 lot - 100 shares). Let's assume that the next Ask is 9.10 @ 1 lot. So the price is now $9.10, given enough participants with views as you the price will move accordingly.
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.