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The most frequent nontrivial example of no-arbitrage bounds is put–call parity for option prices. In incomplete markets, the bounds are given by the subhedging and superhedging prices. [1] [2] The essence of no-arbitrage in mathematical finance is excluding the possibility of "making money out of nothing" in the financial market.
In a discrete (i.e. finite state) market, the following hold: [2] The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space (,,) is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
The absence of arbitrage is crucial for the existence of a risk-neutral measure. In fact, by the fundamental theorem of asset pricing, the condition of no-arbitrage is equivalent to the existence of a risk-neutral measure. Completeness of the market is also important because in an incomplete market there are a multitude of possible prices for ...
This theorem provides mathematical predictions regarding the price of a stock, assuming that there is no arbitrage, that is, assuming that there is no risk-free way to trade profitably. Formally, if arbitrage is impossible, then the theorem predicts that the price of a stock is the discounted value of its future price and dividend:
No free lunch with vanishing risk (NFLVR) is a concept used in mathematical finance as a strengthening of the no-arbitrage condition. In continuous time finance the existence of an equivalent martingale measure (EMM) is no more equivalent to the no-arbitrage-condition (unlike in discrete time finance), but is instead equivalent to the NFLVR-condition.
Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors compare interest rates available on bank deposits in two countries. [1] The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from covered interest arbitrage .
"Arbitrage" is a French word and denotes a decision by an arbitrator or arbitration tribunal (in modern French, "arbitre" usually means referee or umpire).It was first defined as a financial term in 1704 by French mathemetician Mathieu de la Porte in his treatise "La science des négociants et teneurs de livres" as a consideration of different exchange rates to recognise the most profitable ...
In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, [ 1 ] it is widely believed to be an improved alternative to its predecessor, the capital asset pricing model (CAPM ...