In
financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on
financial portfolio prices. These price bounds are a specific example of
good–deal bounds Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if A is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function \rho: ...
, and are in fact the greatest extremes for good–deal bounds.
The most frequent nontrivial example of no-arbitrage bounds is
put–call parity for option prices. In
incomplete market In economics, incomplete markets are markets in which there does not exist an Arrow–Debreu security for every possible state of nature. In contrast with complete markets, this shortage of securities will likely restrict individuals from transfer ...
s, the bounds are given by the subhedging and
superhedging price The superhedging price is a coherent risk measure. The superhedging price of a portfolio (A) is equivalent to the smallest amount necessary to be paid for an admissible portfolio (B) at the current time so that at some specified future time the va ...
s.
The essence of no-arbitrage in mathematical finance is excluding the possibility of "making money out of nothing" in the financial market. This is necessary because the existence of arbitrage is not only unrealistic, but also contradicts the possibility of an economic equilibrium. All mathematical models of financial markets have to satisfy a no-arbitrage condition to be realistic models.
See also
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Box spread
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Indifference price In finance, indifference pricing is a method of pricing financial securities with regard to a utility function. The indifference price is also known as the reservation price or private valuation. In particular, the indifference price is the price ...
References
Mathematical finance
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