...in plain English and mathematically speaking. There are many types: model dependent and independent, statistical, static, dynamic...P

roughly, riskless arbitrage is the possibility of making a sure profit without taking any chances, which should be impossible in rational marketsin the Black-Scholes context this appears in the fact that the perfectly hedged portfolio should have a return equal to the risk free rate of return otherwise one could buy the undervalued asset and short the overvalued one and make a riskless profit

I 'd change "making a sure profit" to "making a sure profit over the risk free rate" as reza himself explains later in the BS framework.rgds,Dimitris

Robert Merton gives a very good definition in one of his papers, which I don't have at hand. In any case, it's something like this:An arbitrage is a series of transactions that provide an initial positive cash flow and that have no possibility of requiring a future negative cash flow.

I would like to add that any arbitrage has to be exploitable. Many times it is not. You may find yourself watching $$$ on your screen but you are unable to seize them!

an arbitrage is a portfolio of zero value today which is of positive value in the future with positive probability and of negative value in the future with zero probability. A static arbitrage is an arbitrage that does not require rebalancing of positions. A dynamic arbitrage is an arbitrage that requires trading instruments in the future, generally contingent on market states. A statistical arbitrage is not an arbitrage but simply a likely profit as predicted by past statistics. MJ

Arbitrage reasoning can be used to value securities, although sometimes in a model dependent way. For example, ifa security price follows geometric Brownian motion, (and markets are frictionless) then anoption on that security can be replicated by dynamically tradingonly the security and a bond. There would be an "arbitrageopportunity" if the market price of the security did not equalthe cost of the dynamic replication. This reasoning yields theBlack-Scholes price for the option.

P.P.S: the phrase "market price of the security" shouldread "market price of the option" (why isn't the edittingenabled ?!!!)

An arbitrage is a multiple trade (that involves buying/selling securities whose price is correlated by a model or a single relation) you can impose the arbitrage relation, when you're able to profit from it, but you cannot expect that other people will impose it for you when you need it. )If one is able to perform arbitrages that means he has some advantages (technical and financial) on other market participants.

as a further sub-classification one could add"risk arbitrage" : a trade designed to capture the convergence in price of two securities due to a proposed merger or takeover.

I'd also add:Model-independent arbitrage = arbitrage (as defined by mj) which does not depend on any mathematical model of financial instruments to work. Eg an exploitable violation of Put-Call parity.Model-dependent arbitrage = does require a model. Eg options mispriced because of incorrect volatility. To see the money here you need to Delta hedge which requires a model.P

GZIP: On