Residual Supply and Demand in Financial Market Models

Summary

The document asks why a finite, arbitrage-free market model might assume that, for any random payoff, some investor is willing to buy it and another is willing to sell it. The answer offers an intuitive market interpretation: noise traders can absorb residual supply or demand, so a counterparty may exist even for an unusual payoff.

Large mutual funds and pension funds are suggested as examples of investors that may take the other side. This is a brief intuition rather than a formal justification: it does not explain how such investors value arbitrary claims, what prices they would accept, or whether the assumption holds in real markets. Its usefulness is therefore mainly conceptual, for understanding a simplifying assumption in mathematical finance.

Key ideas

• The model assumes buyers and sellers exist for any random payoff.
• Noise traders can be viewed as absorbing residual market supply or demand.
• Large mutual funds and pension funds are offered as possible counterparties.
• The explanation is intuitive and does not establish that every payoff has a real-world market.

Tags

# Answer by phdstudent (score 1)


# "For any random variable $X$, someone will be willing to buy and someone to sell a financial instrument, whose final payoff is $X$."












> we will assume that for any random variable $X:\Omega\rightarrow\mathbb{R}$, some investor will be willing to buy and some investor will be willing to sell a 'financial instrument' whose final payoff is $X$. (Actually, this is one of the few assumptions about the market that we have made that is actually plausible.)

This quote is taken from Steven Roman's "Introduction to the Mathematics of Finance Arbitrage and Option Pricing", 2nd edition, Springer 2012.

Why is this a plausible assumption? (The market model under discussion in this part of Roman's book is a finite model (finite time, finite probability space, finite number of assets) with no arbitrage opportunity.)

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/23167

You can think about them as noise traders in the sense of Glostem and Milgrom (1985). It it is a fairly wide used assumption that there is someone out there that soaks up residual supply/demand.

Usually one thinks about this guys as large mutual funds or pension funds.

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.