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I know it is a pretty basic question and I can get this result with BS, however I don't understand it conceptually.

As the time approaches maturity, it is less likely to end out of the money, so I would say that the option value should be higher (positive theta), as it is almost sure that you will exercise it. Could you help me with what I'm missing here?

Many thanks!

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    $\begingroup$ You lose both upside and downside. $\endgroup$
    – Bob Jansen
    Oct 6, 2021 at 18:58
  • $\begingroup$ Thanks for your reply, that make sense. However, the option price decreasing as we are approaching maturity assumes slightly higher odds that the share price will go up. If I'm not mistaken, that should be due to the risk-free r, right? If that is the case, why having an option F1 with a longer time to expiration would give a higher expected profit than another one F2 with a shorter time and reinvesting the earnings after the expiration in a risk-free bond? Apologies if my questions are silly, but I have very little experience working with these concepts. $\endgroup$
    – vsg
    Oct 7, 2021 at 8:35

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The value of an option is based on its intrinsic value plus its time value. Intrinsic value is simply based on, for example for a plain option, the strike price of the option and the underlying instrument’s spot price. Intrinsic value remains unchanged as the maturity is approached as long as the underlying instrument’s price remains unchanged. Time value, however, comes from the potential volatility range of the underlying instrument’s price in the period up to the maturity. As the maturity is approached, time value is decreased because the potential volatility range is reduced and therefore the value of the option.

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