The bid–ask matrix is a matrix

Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

 with elements corresponding with exchange rates between the assets. These rates are in physical units (e.g. number of stocks) and not with respect to any numeraire

Numéraire

Numéraire is a basic standard by which values are measured. Acting as the numéraire is one of the functions of money, to serve as a unit of account: to measure the worth of different goods and services relative to one another, i.e. in same units...

. The element of the matrix is the number of units of asset which can be exchanged for 1 unit of asset .

Mathematical Definition

A matrix is a bid-ask matrix, if

1. for . Any trade has a positive exchange rate.
2. for . Can always trade 1 unit with itself.
3. for . A direct exchange is always at most as expensive as a chain of exchanges.

Example

Assume a market with 2 assets (A and B), such that units of A can be exchanged for 1 unit of B, and units of B can be exchanged for 1 unit of A. Then the bid–ask matrix is:

Relation to solvency cone

If given a bid–ask matrix for assets such that and is the number of assets which with any non-negative quantity of them can be "discarded" (traditionally ). Then the solvency cone

Solvency cone

The solvency cone is a concept used in financial mathematics which models the possible trades in the financial market. This is of particular interest to markets with transaction costs...

is the convex cone spanned by the unit vectors and the vectors .

Similarly given a (constant) solvency cone it is possible to extract the bid–ask matrix from the bounding vectors.

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