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Hi: I am studying arbitrage pricing, and read some sentences in a book as below:It is natural for a new starter to use expectation pricing whereby the price of an asset today (for instance a derivative) is related to the expected future cash flows that the asset will generate. Although intuitive, this is not the method employed in practice. Such pricing mechanisms generate arbitrage opportunities in the market and the consensus is that any acceptable pricing mechanism should not do this. I tried to come up with an arbitrage strategy under the binomial model using expectation pricing V(t=0) = -Call(t=0) + a S(t=0) a is the number of shares of stock = -E[S(t=1)] + a S(t=0) = 0 so a = E[S(t=1)] /S(t=0)V(t=1,w1) = -Call(t=0, w1) + a S(t=1, w1) = K - S(t=0)u + a S(t=0)u = K - S(t=0)u + E[S(t=1)]u which may not necessary non-negative. V(t=1,w2) = Call(t=0, w2) + a S(t=1, w2) = 0 + a S(t=0)d > 0 So I cannot come to an arbitrage. please help. thanks a lot.

One probably will be disagree with the point as far as it contradicts existing benchmark. On the other hand I think that primary drawbacks stems from :*) "The use of expectation pricing"1. This assumption withing derivatives pricing leads to misleading. I could specify if will be asked.The current spot price given a distribution of future prices for either instrument reflects market estimate of the future return. In such interpretation there is no expected value used." Arbitrage pricing."2. Arbitrage is a property of correct pricing and has a sense with the deterministic setting. In stochastic setting higher return always implies higher risk and market provides their balance-reconciliation. In existing derivatives pricing arbitrage has larger importance mainly because the hypothesis that price is expectation or discounted expectation.

thanks a lot! could u pls say more about the misleading of "The use of expectation pricing"?

If the assumption that the price is the expected value of future flow is accepted then this mean this hypothesis is true at any moment of time 0<t<infinity. If we consider a price that forms by a stock which distribution is governed by a log normal law with constant coefficients than this assumption eliminates diffusion and stochastic factors. Indeed at any moment of the future 'u' the stock price is conditional expectation of the future flow with respect to sigma algebra generated by the past observations over stock price. This log-normal equation will reduced to the ordinary dif. eq. One could argue that pricing method for derivatives and stock is different issues. Nevertheless the definition of the notion 'price' should be the same though its formulas are different.

If a stock or other instrument price is expectation of something then they all should have risk free return , otherwise one could construct arbitrage. Given nonrandom risk free return all market instruments should have this return. This idea was the underlying of the option pricing. Hence all derivatives regardless of the real underlying returns becomes very similar. This is an example how the hypothesis about expectation pricing that does not related to derivatives pricing has deformed pricing derivatives and credit derivatives.