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I was reading on risk neutral valuation and i ran into this statement "according to the law of one price , if you have two assets with identical expected cash flow , their current prices must be the same( in a perfect market) otherwise we would have arbitrage" My question: what if the realized cash flow is different from expected cash flow ? So we may not only have arbitrage profit , also there could be a loss and im wondering that why we are not supposed to consider the fact that there is risk i know that in risk neutral method we dont consider the risk preferences but i cant understand What the logic and intuition behind of doing so is , what is the benefit (except for simplifying) ? And ok, we dont consider the risk preferences but the risk exists and even in a risk neutral world we are able to sense the losses originated from risk (for example in this arbitrage case i mentioned above) so why dont we consider it ?

matin keramiyan
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  • Arbitrage is positive profit for certain with 0 initial investment. There is no such thing as arbitrage profit accompanied by arbitrage loss, because arbitrage only happens if profit is for certain. – Mild_Thornberry Dec 17 '19 at 15:59
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    Your source is sloppy. If the expected payoff is the same but the payoffs of the two assets are different in some future state(s) of the world (eg. it is possible that one asset does better than expected while the other does worse), I do not think we have arbitrage. If the payoffs are state-wise identical, (ie. the two assets are perfect subsitutes in every situation).we do – Alex C Dec 17 '19 at 20:24

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