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.).

  • 1
    $\begingroup$ 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". $\endgroup$
    – rajah9
    May 17, 2011 at 16:54

2 Answers 2


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:

  1. 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.
  2. 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.


The differential equation guarantees no arbitrage. There is no need to list each one individually.


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