No-Arbitrage Principles in Derivatives

Arbitrage-free pricing rests on the premise that identical payoffs must have identical prices, within a tolerance band of approximately +/- 2 basis points for liquid instruments. When prices deviate beyond this band, arbitrageurs—acting as air-traffic controllers of financial markets—execute trades that force convergence. Understanding the replication mechanics and funding constraints that enable or prevent arbitrage is essential for pricing derivatives accurately.

Replication Portfolio with Explicit Legs

A replication portfolio constructs the derivative payoff using simpler instruments. The no-arbitrage condition states that the derivative's price must equal the cost of the replicating portfolio.

Forward Replication Example:

To replicate a long forward contract on a stock (no dividends):

The replicating portfolio costs zero at inception and delivers S_T - F at maturity, where F = S₀ × e^(rT).

Three-Leg Basis Spread Example:

Consider a basis trade exploiting a 5 bps mispricing between a future and its synthetic:

The arbitrageur captures 1 bp net after accounting for funding costs.

Cash-and-Carry Funding Workflow

Cash-and-carry arbitrage involves buying the underlying and selling the derivative, financing the spot purchase until delivery.

Workflow:

1. Identify mispricing: Future trades at F > S₀ × e^((r+s)T), where s = storage cost (if applicable)
2. Execute spot leg: Purchase underlying at S₀
3. Finance position: Borrow at repo rate r (e.g., 5.25%)
4. Sell derivative: Short the future at F
5. Hold to convergence: Deliver underlying at expiration
6. Realize profit: F - S₀ × e^(rT) net of financing

Funding Parameters:

• Borrow rate: 5.25% (525 bps)
• Haircut on collateral: 2% (reduces borrowing capacity)
• Repo term: 90 days
• Effective funding cost: 5.25% + haircut impact ≈ 5.35%

If F exceeds fair value by more than 2 bps after all costs, the arbitrage is viable.

Constraints That Break Parity

Several frictions prevent perfect arbitrage:

Short-Sale Constraints:

• Securities may be hard to borrow or unavailable
• Short-sale rebate may be negative (special stocks)
• Uptick rules in certain jurisdictions

Funding Haircuts:

• Collateral is valued below market (e.g., 98%)
• Reduces capital available for financing
• Creates asymmetry between cash-rich and leveraged arbitrageurs

Transaction Costs:

• Bid-ask spreads on spot and derivative
• Exchange and clearing fees
• Slippage on execution

Credit and Counterparty Limits:

• Repo lines have capacity constraints
• Prime broker exposure limits
• Clearinghouse margin requirements

These frictions create tolerance bands within which mispricings persist without arbitrage correction.

Arb Hygiene Controls

Maintaining disciplined arbitrage execution requires:

• Pre-trade verification: Confirm all legs can execute at quoted prices before committing
• Funding lock: Secure financing terms before executing spot leg
• Slippage budgets: Cap execution deviation at 0.5 bps per leg
• Basis monitoring: Track convergence daily with escalation at +/- 3 bps deviation

Control processes ensure that apparent arbitrage opportunities survive transaction costs and execution realities.

Mispricing Cleanup Example

During the March 2020 market dislocation, S&P 500 futures traded at significant discounts to fair value—basis reached -100 bps intraday. Arbitrageurs faced constraints:

• Repo markets seized (funding unavailable)
• Short-sale halts on ETFs
• Margin calls consumed capital

As funding normalized, arbitrageurs rebuilt positions. Basis compressed from -100 bps to -5 bps over two weeks. This demonstrates that no-arbitrage is enforced by market participants, not by mathematical necessity, and depends on functional funding markets.

Next Steps

To apply no-arbitrage concepts to options, see Put-Call Parity Applications.

For futures-specific pricing relationships, review Futures Contract Specifications and Standardization.