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
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.
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