When Option Prices Can Fall Below Intrinsic Value
Summary
The document examines whether an option’s market price must always be at least its intrinsic value. The intuitive arbitrage argument is not universally sufficient: exercise rights, timing, financing, and trading frictions affect whether an apparent discount can actually be captured. For an American option, immediate exercise can generally prevent a price below intrinsic value from persisting in frictionless markets, while transaction costs can complicate the practical comparison.
European options cannot be exercised early, so their prices need not always exceed intrinsic value. The discussion gives a Black–Scholes example in which a deep in-the-money European put is priced below its intrinsic value, and derives a lower-bound condition using a portfolio of stock and put held to maturity. It also notes that limited-upside claims, such as digital options, challenge simple intrinsic-value intuitions. These are model-based and conceptual illustrations; real bid prices may be affected by short-sale constraints, costs, and market conditions, so an apparent discount does not by itself establish an executable arbitrage.
Key ideas
- Intrinsic value alone does not guarantee that every option’s market price is higher under all contract types and trading conditions.
- Early exercise rights can support the intrinsic-value floor for American options in frictionless settings.
- A European put may trade below intrinsic value because it cannot be exercised before expiry.
- A stock-and-put portfolio held to maturity yields a lower-bound condition that accounts for discounting.
- Transaction costs and short-sale constraints can prevent a theoretical price discrepancy from being a practical arbitrage.
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Full text
# True or False? An option's price will always be greater than or equal to its intrinsic value # True or False? An option's price will always be greater than or equal to its intrinsic value Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then exercising it... Consequently, an option's price will always be greater than or equal to its intrinsic value Am I right or wrong in this? ## Answer by Homunculus Reticulli (score 3, accepted) https://quant.stackexchange.com/a/2680 You answered your own question with the statement it began with: "Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then exercising it..." An options price cannot be lower than its intrinsic value (for any discernab,le amount of time - assuming markets remain open and transactions are occuring), for the simple reason that it will represent "free money" - it will be arbitraged away immediately, as you quite rightly noted in your question. ## Answer by Olivier (score 6) https://quant.stackexchange.com/a/2912 In kamikaze_pilot's defense, the question is not that naive or simple. First of all, you need to define what options you are talking about. Consider a digital option for example (which is really fairly vanilla since you can proxy it as a combination of two European calls), which pays 1 of the stock is beyond a certain level at maturity and nothing otherwise. The intrinsic value of the option is just 1 or 0, but would you pay more than 1 to buy such an option ? (what's the point of paying more than whatever you would get at most as a payoff....) In fact, there is a general point here, a option with a limited upside can have a price lower than the intrinsic value. And this may even apply to European vanilla options, although in very specific circumstances: take a European put option with 0.5y to maturity, 20% implied vol, 100 strike and 5% risk-free rate (ignore all dividends for this example). Now for various spot level, calculate the intrinsic value ( Max(0,strike - spot)) and compare to the option price which you can calculate using Black-Scholes: spot = 90 --> intrinsic = 10, option price = 11.04 --> intrinsic < option price spot = 50 --> intrinsic = 50, option price = 47.55 --> intrinsic > option price spot = 10 --> intrinsic = 90, option price = 87.53 --> intrinsic > option price Of course, this only happens for deep in-the-money put options. Also it can not happen for American options (there would definitely be an arbitrage here, since you could by the option and exercise it right away). In terms of arbitrage, consider the following: At time t = 0, your underlying spot is S(0). You buy the stock and a European put option with maturity T and strike K. At time T (maturity), the stock is worth S(T) and your portfolio is either 1) (K - S(T)) + S(T) = K, if S(T) < K 2) or S(T), if S(T) > K If risk-free rate is r, the accrued cost of the portfolio you set up at time 0 is (P(0) + S(t)) * exp(rT). To avoid arbitrage, you need this cost to be greater than the minimum of 1) and 2) above, which is K. You get (P(0) + S(t)) * exp(rT) > K --> P(0) > K*exp(-rT) - S(0). This is the actual arbitrage condition, which is close to saying the intrinsic value is a lower bound of the put option but not quite. ## Answer by bill_080 (score 2) https://quant.stackexchange.com/a/2683 It is common for the Bid (and sometimes the average of the Bid/Ask) price of deep in the money options to be below the Intrinsic Price. Download some data and try it. http://www.cboe.com/delayedquote/QuoteTableDownload.aspx ## Answer by Joshua (score 2) https://quant.stackexchange.com/a/8995 False. It is not always the case for European options which cannot be exercised early and for Americans when you include transaction costs. ## Answer by Julian (score -1) https://quant.stackexchange.com/a/28401 In reality, european option's premium surely can be less than its intrinsic value which is due to short sell is not free...
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