Static Arbitrage Requires No Portfolio Rebalancing

Summary

The document defines static arbitrage by whether positions need to be changed after the initial trade. A static arbitrage is established with a portfolio that requires no subsequent rebalancing; an example is trading different-sized futures contracts in quantities that offset their exposure when their prices violate the expected relationship. Forward price arbitrage is also cited as an example.

Dynamic arbitrage, by contrast, requires future trades, often in response to changing market conditions. Continuous delta hedging of an underpriced option in an idealized Black–Scholes setting illustrates this distinction. The discussion also separates these terms from statistical arbitrage, which describes a profit opportunity inferred from historical patterns, and from model-independent versus model-dependent arbitrage. These labels classify different properties of an opportunity and should not be conflated. The examples are conceptual; they do not address transaction costs, execution risk, or whether a real market discrepancy can be captured profitably.

Key ideas

• Static arbitrage uses positions that need no later rebalancing.
• Dynamic arbitrage depends on future trades, often contingent on market states.
• Offsetting differently sized futures contracts can illustrate a static arbitrage when their pricing relationship is violated.
• Continuous delta hedging is an example of a dynamic strategy in an idealized option-pricing setting.
• Statistical and model-dependent classifications describe different features from the static-versus-dynamic distinction.

Tags

# What‘s the definition of static arbitrage?


# What‘s the definition of static arbitrage?












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!

## Answer by meh (score 2, accepted)

https://quant.stackexchange.com/a/19036

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.

## Answer by user16891 (score 7)

https://quant.stackexchange.com/a/19037

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

- A static arbitrage is an arbitrage that does not require rebalancing of positions.For example static-arbitrage bounds on the Prices of Basket Options

- A dynamic arbitrage is an arbitrage that requires trading instruments in the future, generally contingent on market states.

- A statistical arbitrage is a likely profit as predicted by past statistics.

- 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.

- Model-dependent arbitrage does require a model. An example would be options mispriced because of incorrect volatility.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.