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Could someone give the strict definition of static arbitrage? I know what the arbitrage means but have no idea about the term "Static".

Thanks in advance!

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A static arbitrage is an arbitrage that does not require any re-balancing of the portfolio. For example, the CME offers a mini euro future for 62,500 euros and a big euro future worth 125,000 euros. You could sell 1 big future and buy 2 mini futures and this would be a static arbitrage. Another example would be the forward price arbitrage.

A dynamic arbitrage is one in which you have to re-balance your portfolio. An example of this would be buying an under priced option in the perfect black-scholes world while continuously delta hedging.

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The definition of arbitrage can be broken down into categories such as:

  1. A static arbitrage is an arbitrage that does not require rebalancing of positions.For example static-arbitrage bounds on the Prices of Basket Options
  2. A dynamic arbitrage is an arbitrage that requires trading instruments in the future, generally contingent on market states.
  3. A statistical arbitrage is a likely profit as predicted by past statistics.
  4. Model-independent arbitrage does not depend on any mathematical model of financial instruments to work. An example of this would be a violation of Put-call parity.
  5. Model-dependent arbitrage does require a model. An example would be options mispriced because of incorrect volatility.
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