I understand that it is possible for a European put option to trade below its intrinsic value (i.e. assuming a positive risk-free rate, the theoretical lower bound of a European put is lower than its intrinsic value). In such cases, the European put option has negative time value. My question is: do European puts sell below intrinsic value in real life? Or is the theoretical lower bound only theoretical?

Note: I have no real-world experience in trading derivatives. My knowledge of derivatives is completely theoretical, hence this question.

  • 1
    The CBOE page on SPX options notes that this is possible for European style put options, and this implies "real world" prices. Interesting. Being Euro style, they cannot be exercised before expiry, so that removes any obvious arbitrage opportunity. Perhaps a sudden spike in the underlying volatility is necessary for such a circumstance. It's hard to imagine how the exchanges pricing models would calculate this outcome.
    – not-nick
    Apr 29, 2020 at 5:36

1 Answer 1


Of course.

While there is a theoretical price of an option, most firms would not be willing to enter into a trade unless they can make a certain amount of profit from the trade, so they would add something extra to the price (a spread).

However, as the arbitrage is quite straightforward (e.g. buying the put, buying the underlying, holding to delivery, exercising, paying the interest) it is likely many firms would be willing to trade it for a small spread, so it would not trade too far below its intrinsic value.

  • 1
    Even if the spread is negligible, a deep-in-the-money European put will trade below intrinsic value by an amount equal to the interest on the strike. Intrinsic value of a put, by definition, means strike minus underlying. It seems like this answer takes "intrinsic value" as meaning "theoretical value" or "fair value" and misses the point by focusing on the spread.
    – nanoman
    Apr 30, 2020 at 5:20

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