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Everyone is giving the same type of answer..here is a different perspective. Put call parity can actually be violated in special cases where a positive drift is established ,which is equal , mathematically speaking, to reflected Brownian motion about some floor value. I've seen a few options that have a risk-free profit that exceeds the interest rates. For ...

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Note that, for small $\delta$, $e^{\delta}= 1+ \delta + O(\delta^2)$ and $\sqrt{x+\delta} = \sqrt{x} + O(\delta)$. Then, \begin{align*} u &= e^{r\Delta t} + e^{r\Delta t}\sqrt{e^{\sigma^2\Delta t} - 1}\\ &= 1+ r\Delta t + O(\Delta t^2) + [1+ r\Delta t + O(\Delta t^2)] \sqrt{ \sigma^2\Delta t +O(\Delta t^2)}\\ &=1+ r\Delta t + O(\Delta t^2) + [1+ ...

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"Intuitively, everything else being equal, if a stock has higher drift, shouldn't it have higher probability of finishing in-the-money (and higher probability of having higher payoff), and the call option should be worth more?" All these other answers are focusing on the wrong aspect of the question - it is true that the maths makes the drift drop out from ...

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The risk neutral drift is the risk free rate for an asset with no dividends, no cost of carry, no repo cost, etc. Otherwise the drift has to be adjusted to take these into account, and the easiest way to do it (when available) is to use forwards (equal to the expected asset value under the forward measure) or futures (equal to the expected asset value under ...

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