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Risk-Neutral Pricing from State-Dependent Asset Payoffs

Article Quant Q&A · Author: Svit
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Summary

The document poses a finite-state pricing question. It gives prices and payoffs across three possible states for three existing assets, then introduces a fourth asset whose payoff is zero in two states and positive in the third. The question asks how to value that new asset using risk-neutral probabilities.

This setup points toward finding state prices or risk-neutral probabilities that reproduce the observed prices of the existing assets, then applying those weights to the new asset’s state-contingent payoff. However, the document contains no worked solution, assumptions, or answer. In particular, it does not establish whether the given assets span the state space, whether the pricing probabilities are unique, or what risk-free discounting convention should apply. It is therefore a useful statement of a basic derivative-pricing problem, but readers must supply the derivation and check whether the available assets determine a unique price.

Key ideas

  • The example specifies payoffs for several assets across a finite set of states.
  • Observed asset prices can be used to infer state prices or risk-neutral probabilities.
  • The new asset’s price depends on its payoff in each state and the inferred state prices.
  • The document does not provide a solution or establish that the implied pricing measure is unique.

Tags

Derivatives pricingOptionsStatistics
Full text
# Risk neutral valuation


# Risk neutral valuation












In a world with three possible states (1, 2, 3) and three assets (A, B, C), the payoff matrix looks like this:

$r_A;_1,_2,_3 = 110, 110, 110$ $p_A = 100$

$r_B;_1,_2,_3 = 100, 50, 40$ $p_B = 70$

$r_C;_1,_2,_3 = 48, 40, 36$ $p_C = 40$

Now we add asset D in portfolio:

$r_D;_1,_2,_3 = 0, 0, 10$ $p_D = ? $

How can one calculate a price of the asset D via risk neutral probability ethod?

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