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I have read that the price of an option is not affected by the drift of the stock since the drift term doesn't appear in the Black Scholes PDE. I become confused because to me, this implies that the future value of the stock does not affect the value of the option, so why should the current value of the stock affect the option price?

math111
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  • Your previous and almost identical question https://quant.stackexchange.com/questions/43778 was closed as off topic for being too basic. Re-posting it doesn't change that. – LocalVolatility Jan 31 '19 at 23:08
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    Downvote for being to basic. Try to look up 'risk-neutral valuation' – Sanjay Jan 31 '19 at 23:33
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    Similar question https://quant.stackexchange.com/questions/8247/why-drifts-are-not-in-the-black-scholes-formula/8252#8252 – user23564 Feb 01 '19 at 00:48
  • Where can I post then so that I can have help understanding why. And if it is basic, shouldn’t it tend itself to a quick and long easy answer to formulate? – math111 Feb 01 '19 at 01:02
  • In any case as user23564 pointed out it's already been answered – Lliane Feb 01 '19 at 02:09
  • Well a simple answer would be, we don't price things in the Physical probability measure. i.e. whenever we are trying to price any tradeable asset, we price is in the risk-neutral probability measure. And when we do this particular transformation.. the mu term changes to r (interest free rate) for all tradeable securities. Which basically is the explanation of the Girsanov Theorem and Risk-neutral pricing. What does that mean? Under BS assumptions you can perfectly hedge the asset, so the market would only compensate you for the risk free rate – user23564 Feb 01 '19 at 02:48

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