Why Deep In-the-Money Calls Can Trade Below Intrinsic Value
Summary
The document examines reports of deep in-the-money calls on a dividend-free ETF trading below intrinsic value, which makes implied volatility difficult to solve under a standard model. The question considers whether a dividend yield assumption or a pricing-model flaw could explain the apparent mismatch, and whether the prices imply an arbitrage opportunity.
One answer points to exercise fees, funding costs, or other costs of holding the position. Such costs can make an option holder willing to sell below theoretical parity, so the discrepancy does not by itself establish a risk-free trade. A second answer describes a market-data example in which each option represented 10,000 underlying units and the displayed bid and ask appeared reversed because of a translation issue. These explanations are specific possibilities, not a diagnosis of every such quote. The document gives no transaction-level evidence or complete arbitrage analysis; contract terms, quote conventions, and executable prices would need to be checked before drawing a conclusion.
Key ideas
- Deep in-the-money calls may appear below intrinsic value when standard pricing inputs do not fit observed quotes.
- Exercise fees can reduce the price a holder is willing to accept for an in-the-money option.
- Funding and other holding costs can also move option prices away from theoretical parity.
- A quote display or translation issue can make bid and ask prices appear reversed.
- An apparent parity gap alone does not demonstrate an executable arbitrage opportunity.
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# Why Are Deep In-the-Money Call Options Priced Below Intrinsic Value in Dividend-Free ETFs? # Why Are Deep In-the-Money Call Options Priced Below Intrinsic Value in Dividend-Free ETFs? I have encountered an unusual situation in the market regarding deep in-the-money call options on dividend-free ETFs. According to standard option pricing theory, the price of a call option should always be greater than its intrinsic value, and its price is typically affected by the dividend yield (q). This is discussed in this thread. However, I am seeing scenarios where the price of the call is actually lower than its intrinsic value in the case of deep in-the-money calls. This would normally only make sense if a dividend yield 𝑞 q were set, but that’s clearly not the case here, as the ETF has no dividends. Here are the key observations: Deep in-the-money calls: The price of the option is less than its intrinsic value, which cannot be explained unless a non-zero dividend yield is assumed. Implied volatility issues: When trying to compute implied volatility for these deep in-the-money calls, I encounter a problem. The volatility cannot be solved properly because even setting the minimum volatility to 0 doesn’t yield the observed price. On the other hand, implied volatility for at-the-money (ATM) or out-of-the-money (OTM) calls is solvable without issue. Effect of dividend yield (q): When I adjust 𝑞 , the deep in-the-money call options start to show reasonable implied volatility values, but this adjustment causes issues with the implied volatility of deep in-the-money put options. I’m wondering why this pricing anomaly occurs and whether there are any potential arbitrage opportunities arising from this situation. Could there be a flaw in the pricing model, or is there an external market factor that’s influencing the pricing of these options in such a way? Any insights or thoughts would be greatly appreciated! ## Answer by Harry Crimmins (score 2) https://quant.stackexchange.com/a/82000 This can happen for several reasons. The reasons that I am aware of are related to fees or funding costs. For example, some exchanges will charge fees for exercising options, and these can be larger than trading fees (e.g. proportional to the strike). In such a case, a holder of ITM calls can be willing to sell them for below parity. Exercise fees are just one example, in general any cost of holding a position can result in options trading away from their 'theoretical value'. ## Answer by Chandler Bing (score 0) https://quant.stackexchange.com/a/81995 Actually, this is based on a real market event, where each option corresponds to 10,000 units of the underlying asset. Even with a risk-free rate ( r = 0 ), the implied volatility still cannot be solved for. Below is a screenshot of the market data: the ETF price is 1.122. It’s important to note that there seems to be a translation issue with the software, as the ask and bid prices have been swapped. It's a bit funny, but I wanted to clarify that here.
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