How Transaction Costs Define Arbitrage Bounds for Related Instruments
Summary
Arbitrage bounds describe the range of prices for a spread among related tradable instruments within which trading costs prevent a profitable arbitrage. The document illustrates this with a package that can be opened into individual units or assembled from them. If the package is sufficiently cheap relative to its components, a trader can buy packages, open them, and sell the units; if it is sufficiently expensive, the reverse trade may be profitable. Redemption and creation costs set the lower and upper limits for the spread.
The same logic applies to index and exchange-traded fund arbitrage: the relevant bounds concern combinations of instrument prices, and transaction costs determine when deviations become actionable. Bounds are not universal fair-value limits, because market participants can face different costs and therefore different profitable-trading thresholds. The example explains the intuition but does not quantify costs or address practical constraints such as execution risk, liquidity, or capital requirements.
Key ideas
- Arbitrage bounds apply to prices or spreads across related instruments.
- Creation and redemption costs set thresholds for profitable trades in opposite directions.
- Index and exchange-traded fund arbitrage follow the same general cost-based logic.
- Different participants may face different costs and therefore different arbitrage bounds.
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Full text
# What exactly are the “bounds” in arbitrage bounds?
# 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?
## Answer by krkeane (score 1)
https://quant.stackexchange.com/a/72244
> 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.
## Answer by Pranav (score 0)
https://quant.stackexchange.com/a/72230
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.