# What exactly are the “bounds” in arbitrage bounds?

Wikipedia’s article on arbitrage bounds is loaded with jargon, and thus requires a lot of prerequisite knowledge to understand what should be a basic definition.

What exactly are the “bounds” in arbitrage bounds? What is being bounded, and what are the extreme ends of the range? Are they prices?

• I agree, the wiki article is really bad. Could you provide more context for your question? I.e. aside from wiki, where does it come from? May 17, 2021 at 21:49
• You may want to have a look at this question where some of these arbitrage bounds are listed. They are upper and lower bounds for option prices and derived on the assumption that the market is free of arbitrage. Avoiding assumptions about the distribution of the stock price, these bounds therefore universally apply to many different models (but are perhaps not quite as tight). May 17, 2021 at 21:53

What exactly are the “bounds” in arbitrage bounds?

The bounds refer to price levels for the combination of related tradable instruments (spreads) outside which arbitrage activity switches from unprofitable to profitable.

Example:

• 3-cookie package price $$p_3$$
• 1-cookie price $$p_1$$
• cost to pay someone to redeem (open) a cookie pack $$c_{\textrm{redeem}}$$
• cost to pay someone to create (seal up) a cookie pack $$c_{\textrm{create}}$$.

Arbitrage-free price lower and upper bound price limits for a cookie / package spread:

• profitably buy cookie 3-packs, open package, sell three single cookies when: $$3 p_1 -p_3 > c_{\textrm{redeem}}$$
• profitably buy three single cookies, seal up package, sell cookie 3-packs when: $$p_3 - 3 p_1 > c_{\textrm{create}}$$
• combining these two equations, the arbitrage upper and lower bounds for this example's cookie spread are: $$-c_{\textrm{create}} < 3 p_1 - p_3 < c_{\textrm{redeem}}$$

Index arbitrage and ETF arbitrage work in an analogous manner, and the transaction costs yield arbitrage bounds. In general, different market participants have different cost structures, and therefore different arbitrage bounds.

Bound is the limit within which arbitrage opportunity opens up. If the charges are frictions are more the bound is larger and chances of arbitrage are more. So ideally the charges if kept well (read low) and reasonable there are no arbitrage opportunities and fair price trading for all.

• So a large price discrepancy between two currencies (which could be arbitraged) would be an example of large arbitrage bounds, correct? Sep 17, 2022 at 13:09
• Ahem... The bounds are the limits outside of which arbitrage opportunity opens up. If price is within bounds no arbitrage exists. Sep 17, 2022 at 14:36