Testing Calendar Arbitrage with Executable Option Quotes

Summary

The question asks whether apparent calendar arbitrage exists between December and January options on the same stock. The researcher compares implied volatilities calculated from top-of-book midquotes and notes that total implied variance should not decrease with expiry under the stated no-calendar-arbitrage condition. The apparent signal persists during the observed trading day, and the question says there are no dividends before expiry.

The answer says to evaluate whether the opportunity survives using executable sides of both markets. For the proposed trade, that means selling the December put at its bid and buying the January put at its offer; the response reports that accounting for the bid-ask spreads removes the apparent arbitrage for the put and call cases. The exchange is a concise warning that midquote-derived volatility comparisons can suggest an opportunity that cannot be captured at tradable prices. It does not provide the quotes, calculation details, or a broader test of calendar-arbitrage conditions, so the conclusion is limited to the cited quote setup.

Key ideas

• The question flags an apparent calendar-arbitrage signal based on midquote implied volatilities across expiries.
• The stated no-arbitrage condition concerns total implied variance across time to expiry.
• Check a calendar trade using executable prices, selling at the near expiry bid and buying the later expiry offer.
• The answer reports that bid-ask spreads remove the apparent opportunity in the described put and call cases.
• Midquote comparisons alone do not establish that an arbitrage can be executed.

Tags

# Is this actual example of calendar arb in quotes?


# Is this actual example of calendar arb in quotes?












From my understanding total implied variance has to be a monotonic function of time for there to be no calendar arbitrage. Stumbled upon quotes for this Monday with apparent arb (NKE Dec expiry vs Jan), not sure if this is correct, but I have checked this across open hours and it looks persistent throughout the day.

Is this even possible? Am I missing something?

Vols are derived from mid of top of the book quotes. There are no divs before the expiry.

## Answer by sle (score 1)

https://quant.stackexchange.com/a/59025

As Will advised to check, there is actually no arb for both put & call considering the spread to be crossed (particularly for Dec expiry) on both legs, ie hitting Dec expiry put wing at bid and lifting Jan at offer.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.