Option No-Arbitrage Bounds and Their Market Frictions
Summary
The document reviews model-independent option pricing restrictions that limit possible prices regardless of a trader’s subjective forecast. It lists put-call parity, the ordering of call prices across strikes, convexity across strikes to rule out negative butterfly spreads, and nonnegative horizontal calendar spreads under low interest rates. These relationships constrain option prices without requiring a specific pricing model.
The replies stress that such conditions are idealizations in actual markets. Bid–ask spreads can make apparent violations consistent with executable prices, and different stock borrowing and lending rates can complicate put-call parity. Counterparty risk is another consideration. One response states that a differential-equation framework can encode no-arbitrage constraints rather than listing each condition separately, but the thread does not elaborate on that approach. The discussion gives no market data or detailed formulas for adjusting bounds, so practical use requires accounting for transaction costs, financing, and credit conditions.
Key ideas
- Put-call parity, strike ordering, strike convexity, and calendar-spread constraints restrict option prices without a specific model.
- Strike convexity rules out negative butterfly spreads under idealized no-arbitrage assumptions.
- Bid–ask spreads can explain apparent violations of model-free pricing relationships.
- Different borrowing and lending rates can create apparent deviations from put-call parity.
- Counterparty risk can also affect whether theoretical arbitrage relationships hold in practice.
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Full text
# What are important model and assumption-free no-arbitrage conditions in options trading? # What are important model and assumption-free no-arbitrage conditions in options trading? In the paper "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula" (Espen Gaarder Haug, Nassim Nicholas Taleb) a couple of model-free arbitrage conditions are mentioned which limits the degrees of freedom for an option trader. The four conditions mentioned in the paper are: - Put-call parity (obviously) - A call with strike $K$ cannot trade at a lower price than call $K+\delta K$ (avoidance of negative call and put spreads) - A call struck at $K$ and a call struck at $K+2*\delta K$ cannot be more expensive than twice the price of a call struck at $K+\delta K$ (negative butterflies) - Horizontal calendar spreads cannot be negative (when interest rates are low) What other such model/assumption-free no-arbitrage conditions exist in options trading? That is, conditions that reduce the degrees of freedom for a rational option trader regardless of his or hers subjective beliefs (such as belief in a certain model, etc.). ## Answer by Brian B (score 5, accepted) https://quant.stackexchange.com/a/1667 You have pretty much hit them all. The no-arbitrage assumption itself is highly unrealistic, though. If you want to enhance your model-free thinking about options, you will have to incorporate at least two important cases where that assumption is false: - Bid-offer spreads are not zero. This means in particular that the four model-free conditions you cite above can be violated within the sum total of spreads involved. - The borrow/lend rate. Since in practice you generally cannot receive the same rate for lending stock that you pay to borrow it, put/call parity (among other prices) will have apparent violations. Counterparty risk can also be a significant model-free consideration. ## Answer by Thomas Baert (score 1) https://quant.stackexchange.com/a/17822 The differential equation guarantees no arbitrage. There is no need to list each one individually.
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