SERVING THE QUANTITATIVE FINANCE COMMUNITY

Paul
Topic Author
Posts: 10789
Joined: July 20th, 2001, 3:28 pm

### What is arbitrage?

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

reza
Posts: 3013
Joined: August 30th, 2001, 3:40 pm

### What is arbitrage?

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

plessas
Posts: 413
Joined: March 9th, 2002, 10:23 pm

### What is arbitrage?

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

Marsden
Posts: 3829
Joined: August 20th, 2001, 5:42 pm

### What is arbitrage?

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.

Anthis
Posts: 4313
Joined: October 22nd, 2001, 10:06 am

### What is arbitrage?

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!

mj
Posts: 3449
Joined: December 20th, 2001, 12:32 pm

### What is arbitrage?

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

Alan
Posts: 10263
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### What is arbitrage?

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.

Alan
Posts: 10263
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### What is arbitrage?

P.S: -- my post is just a variation on reza's earlier post

Alan
Posts: 10263
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### What is arbitrage?

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

gerico
Posts: 43
Joined: September 21st, 2002, 8:37 am

### What is arbitrage?

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.

filthy
Posts: 338
Joined: April 25th, 2002, 7:34 am

### What is arbitrage?

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.

Paul
Topic Author
Posts: 10789
Joined: July 20th, 2001, 3:28 pm

### What is arbitrage?

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