Derivatives
Arbitrage Free and Why Prices Must Stay Consistent
Financial markets do not require prices to be fair. They only require prices to be consistent. The concept of arbitrage free sits at the heart of this idea.
An arbitrage-free market is one where no riskless profit can be made using zero initial investment. This assumption underpins almost every pricing model used in finance.
Exams test this concept repeatedly, often without using the word arbitrage directly.
What Arbitrage Free Really Means
A market is arbitrage free when there is no opportunity to earn a guaranteed profit without risk and without capital.
If such an opportunity existed, traders would exploit it immediately. Their actions would push prices until the opportunity disappeared.
Arbitrage free does not mean markets are perfect. It means obvious mispricing does not persist.
Why Arbitrage Forces Matter
Arbitrage is a discipline mechanism.
When two assets with the same payoff are priced differently, arbitrageurs buy the cheaper one and sell the expensive one. This trading pressure aligns prices.
This logic explains why pricing relationships hold across markets, instruments, and time.
Arbitrage Free as a Pricing Foundation
Many pricing formulas are not derived from investor preferences. They are derived from arbitrage arguments.
Forward prices, futures prices, option bounds, and swap rates all rely on the assumption that arbitrage opportunities are absent.
Exams often test whether candidates recognise when a pricing relationship violates arbitrage-free conditions.
Arbitrage Free Does Not Mean No Risk
This is a common confusion.
Arbitrage free does not mean investors cannot lose money. It means profits are not guaranteed.
Risky trades can still generate losses. Prices can still be volatile. What cannot persist is a trade that delivers certainty without cost.
Arbitrage Free vs Market Efficiency
Arbitrage free is a weaker condition than market efficiency.
Markets can be arbitrage free even when prices do not reflect all available information. Efficiency requires information to be fully reflected. Arbitrage free only requires that blatant pricing inconsistencies are eliminated.
Exams sometimes test this distinction subtly.
How Arbitrage Appears in Exam Questions
You may see:
- two assets with identical payoffs but different prices
- a forward price that violates cost-of-carry logic
- an option price outside theoretical bounds
In each case, the correct response relies on arbitrage-free reasoning.
Common Student Errors
Students often:
- assume arbitrage free means fair pricing
- ignore transaction costs when thinking about arbitrage
- confuse arbitrage with speculation
These errors frequently appear as incorrect options.
Final Perspective
Arbitrage free markets are defined by consistency, not perfection. Prices adjust because traders exploit guaranteed profit opportunities until they vanish. For exam preparation, the key is to recognise when prices violate basic payoff logic. Once that skill is developed, many valuation and derivatives questions become straightforward.
