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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.
When stock price returns follow a single Brownian motion, there is a unique risk neutral measure.When the stock price process is assumed to follow a more general sigma-martingale or semimartingale, then the concept of arbitrage is too narrow, and a stronger concept such as no free lunch with vanishing risk (NFLVR) must be used to describe these opportunities in an infinite dimensional setting.
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 ...
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.
If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium, or an arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. The "no arbitrage" assumption is used in quantitative finance to calculate a unique risk neutral price for derivatives ...
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:
Under the no-arbitrage assumption, the net premium paid out to acquire this position should be equal to the present value of the payoff. Box spreads' name derives from the fact that the prices for the underlying options form a rectangular box in two columns of a quotation.
No arbitrage opportunity (i.e., there is no way to make a riskless profit). Ability to borrow and lend any amount, even fractional, of cash at the riskless rate. Ability to buy and sell any amount, even fractional, of the stock (this includes short selling). The above transactions do not incur any fees or costs (i.e., frictionless market).