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nobody had bought or sold that specific option since then $485 would still be the "latest price" even if it was wildly out of date.
