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Trader bought a one month $150 strike CALL OPTION on stock XYZ that is trading for $150. He paid $500 for the contract. After two days, the stock's price is $160 but the trader sees that his contract value is less than $500. Let us say it is $485.

What caused the contract value to drop from $500 to $485 even though the underlying stock price went higher from $150 to $160? My understanding is that Time Decay has not happened so the Option Value should not go down $15 for the contract.

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    Usual answer here is underlying implied volatility has changed, which can often change the value of an option substantially more than a move in the actual stock price. – Philip Dec 15 '20 at 13:10
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    @Fattie - (1) This isn't a homework question. The OP has been asking option questions here for the past 9 months. (2) Questions aren't closed because of typos or if they are about trivial issues to you. (3) It's presumptuous for you to conclude that this "question has no value to anyone wanting to know about these topics", that is, unless you are Carnac the Magnificent. – Bob Baerker Dec 15 '20 at 14:35
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    @BobBaerker .. "The OP has been asking option questions here for the past 9 months" Fair enough, I did not notice - removed. Do note that copy-paste "homework questions" are "not allowed" on SE sites (inc. this one I think?) - but apparently I was mistaken and this is Not Homework. Hooray! Usually on the "close selector" there's an option "Not reproducible or was caused by a typo While similar questions may be on-topic here, this one was resolved in a way less likely to help future readers." (I just copied that from another site), so I was trying to type that from memory :) :) – Fattie Dec 15 '20 at 14:40
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    "but the trader sees that his contract value is less than $500. Let us say it is $485." Is this based on last sale price? Midpoint between bid and ask? – Lou Dec 15 '20 at 15:51
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    @Lou - It depends on what you are looking at. Last Price is simply the price at which the last trade occurred. If you're looking at position value on your account value page at your broker, that tends to be the midpoint between bid and ask price. – Bob Baerker Dec 16 '20 at 19:19
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Your scenario is impossible because an option that is $10 in-the-money will be worth at least $10, so one possibility is stale option prices, but let's take the directional moves and see what could have caused it.

The most common model used to price options is the Black-Scholes model or variants. With the B-S model, there are 5 input variables:

  • Strike
  • Underlying Price
  • Time to Maturity
  • Interest Rate
  • Volatility

When the Underlying Price goes up, so does the price of a call. TTM and IR have very small effects over 2 days with a month to maturity, so the only thing that could have caused the price to go down is Volatility, since Strike is constant in this case.

When volatility goes up, option prices go up (more uncertainty), so if an option price goes down when the underlying goes up, the only explanation is that the expected (implied) volatility went down, and that change had more effect than the effect of the underlying going up.

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  • TTM can have a huge impact if the option mature within days. The relative change is relevant, 2 days of 3 remaining will heavily impact the prices; 2 of 150 days remaining little. – Aganju Dec 15 '20 at 21:09
  • @Aganju True, but a month out (as stated in the question) it doesn't. I've clarified that in the question, though. – D Stanley Dec 15 '20 at 21:37
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The theta of this call option would be about -0.09 so the expectation would be about 18 cents of time decay in two days. After that, your question has gone off the rails.

If you buy a $150 call for $5 when the stock is $150 and the stock rises $10 to $160 in two days then the intrinsic value of the call is $10 and the price of the call would be over $10. With no change in implied volatility, it would be worth about $11.50 not $4.85. It would not decrease in value. Perhaps you might want to rethink the parameters of your question.

As suggested in Philip's comment, change in implied volatility can make an option move in the opposite direction as share price (stock up and call price down or stock down and put price up) but that interaction cannot violate intrinsic value.

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If it is a thinly-traded option (quite possible for non-standard strikes/expiries in most stocks), then this is most likely a trade from one or two days ago.

If nobody had bought or sold that specific option since then $485 would still be the "latest price" even if it was wildly out of date.

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    Yes, a stale quote from some number of days ago would be the Last Price but it would not be the current NBBO price which any broker would quote during regular trading hours, reflecting a minimum of $10 of intrinsic value which was explained in other answers. – Bob Baerker Dec 15 '20 at 23:42

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