In
financial mathematics
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the Finance#Quantitative_finance, financial field.
In general, there exist two separate ...
, no-arbitrage bounds are mathematical relationships specifying limits on
financial portfolio prices. These price bounds are a specific example of
good–deal bounds, and are in fact the greatest extremes for good–deal bounds.
The most frequent nontrivial example of no-arbitrage bounds is
put–call parity
In financial mathematics, the put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a shor ...
for option prices. In
incomplete markets, the bounds are given by the subhedging and
superhedging prices.
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 persistent risk free
arbitrage
Arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more marketsstriking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which th ...
opportunities 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
*
Indifference price
References
Mathematical finance
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