Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.).

share|improve this question
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
up vote 4 down vote accepted

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.

share|improve this answer

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

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.