Hi

@Eustice_Langham Thank you for liking the video! The call option delta is given by exp(-qT)*N(d1) where q is the dividend yield such that, in the case of a non-dividend-paying stock, the Δ reduces to N(d1). Even when there is a dividend yield, exp(-qT) is almost 1.0 so that N(d1) approximates regardless.

N(.) is the standard normal cumulative distribution function. In my XLS, like others, I am simply using =NORM.S.DIST(z,TRUE) = =NORM.S.DIST(

**d1**,TRUE). So the shape of call option delta

**is literally the shape of a normal CDF**; see right-hand panel

https://en.wikipedia.org/wiki/Normal_distribution
Notice that put Δ = N(d1) - 1, so it's shape is also the shape of the normal CDF but just happens to be shifted down by -1.0, below the X-axis.

BTW, if you take the derivative of a CDF, get the corresponding density PDF; in the case of the normal, that's the familiar bell-shaped distribution. The option's greek vega is given by v = S(0)*sqrt(T)*N'(d1) where N'(.) is the probability density function for a standard normal; ie, the first derivative of N(.). For this reason, vega has a shape that resembles the normal PDF, although not exactly due to the S(0)*sqrt(T) multiplier. I hope that's interesting, thanks,

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