Skip to content
All library documents

Market Completeness, Replication, and Risk-Neutral Measure Uniqueness

Article Quant Q&A · Author: Andrei
Read the original

Summary

The document defines a complete market as one in which every derivative payoff can be replicated using positions in the traded securities. Replication makes it possible, in principle, to hedge away the uncertainty in a derivative by trading those securities. The discussion points to stochastic calculus literature for an algebraic treatment of the definition.

It also states the central connection between completeness and the uniqueness of the risk-neutral measure: in the framework referenced, the two properties correspond one to one. The original question asks whether perfect competition is among the requirements, but the answer does not provide an exhaustive list of assumptions or discuss competition. As a result, this is a concise conceptual pointer rather than a full set of market conditions or a practical test for whether a particular market is complete.

Key ideas

  • A market is complete when every derivative payoff can be replicated with traded securities.
  • Replication provides a hedge that removes derivative payoff uncertainty in the model.
  • Market completeness is linked to uniqueness of the risk-neutral measure.
  • The response does not specify an exhaustive list of assumptions or address perfect competition.

Tags

Derivatives pricingRisk managementStatistics
Full text
# Conditions for market completeness


# Conditions for market completeness












We know that a market is called complete if it is possible to replicate any future payoff trading in its securities. Is there an exhaustive list of requirements that when satisfied imply market completeness? Is perfect competitiveness one of those?

## Answer by KT8 (score 1)

https://quant.stackexchange.com/a/75718

A market is said to be complete if every derivative can be hedged. You can find a discussion of this, e.g. in Shreve's Stochastic Calculus for finance II (chapter 5). The idea is that then you can remove any source of uncertainty/risk (i.e. hedge) from the derivative in that market by taking some positions in the securities that belong to that market.

In that book he also gives an algebraic definition and discusses why that claim is mapped one to one to the uniqueness of the risk neutral measure.

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.