Risk-Neutral Valuation, Arbitrage, and Risky Cash Flows

Summary

The document presents a conceptual question about risk-neutral valuation and the law of one price. It asks how equal expected cash flows could imply equal current prices, given that realized cash flows may differ and a trade intended to exploit a price discrepancy could still incur a loss. It also asks why valuation under a risk-neutral measure appears to set aside risk preferences when uncertainty remains.

No answer or valuation method is supplied, so the text does not establish that assets with equal expected cash flows must have equal prices in general. The issue points toward the key distinction between matching expected cash flows and matching state-contingent payoffs: arbitrage requires a suitably hedged payoff relation, while risk-neutral pricing uses a pricing measure consistent with no-arbitrage assumptions. Readers will need further material to resolve the question’s premises and understand when the framework applies.

Key ideas

• The document questions how risk-neutral valuation relates to uncertain realized cash flows.
• Equal expected cash flows alone do not establish an arbitrage relationship between assets.
• Arbitrage reasoning depends on comparing payoffs across states, not only their expectations.
• The text poses the role of risk preferences but does not provide an answer.

Tags

# Risk neutral valuation logic/intuition


# Risk neutral valuation logic/intuition












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 ?

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