# 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.).

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Great paper! Point 4 is interesting in a futures context. Futures markets usually display contango, namely a positive sloping curve with further out contracts. This makes sense because of cost of carry and storage fees. However, you will occasionally get the opposite, backwardation, with a negative sloping curve. There have been times when a 3-month T-bill > 10-yr (inverted yield curve) and when West Texas Intermed. spot has been greater than the WTI futures contract (such as when a hurricane is heading toward the Gulf). One says "recession coming"; the other says "get that oil outta Texas". –  rajah9 May 17 '11 at 16:54