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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.
If in a financial market there is just one risk-neutral measure, then there is a unique arbitrage-free price for each asset in the market. This is the fundamental theorem of arbitrage-free pricing. If there are more such measures, then in an interval of prices no arbitrage is possible.
"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 ...
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.
9. Set up an annuity. An annuity can be a good place to set up reliable income. With a typical annuity, you make payments to an insurance company, which will provide you with a stream of income in ...
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of ...