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
In finance, a portfolio is a collection of investments.
Definition
The term "portfolio" refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial profess ...
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
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 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 transferr ...
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 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
*
*
Box spread
In options trading, a box spread is a combination of positions that has a certain (i.e., riskless) payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread constructed from calls (e.g., long a 50 call, s ...
*
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 pric ...
References
Mathematical finance
{{econ-stub