I liked this article (W Technical Article), nice way of deriving Black-Scholes. (I also like their book)

Some minor comments:

On page 5: under the Exercise, it is a reference to the excellent Corrado & Su paper on the Gram-Charlier expansion. The reference to the Q3 and Q4 are correct, but unfortunately there was an error/typo in the original paper, so Mike you also got this wrong (never trust papers even in top journals ).

The last part of Q3

-(vol*Sqrt(T))^2N(d1)]

should be

+(vol*Sqrt(T))^2N(d1)]

this correction is forthcoming by Christine A. Brown and David M. Robinson in same journal as the Corrado & Su paper.

To get a put value one can simply use the anti-matter input , that is negative vol and change sign of skewness, kurtosis will stay the same, then multiply by minus one. (W Technical Article)

Warning: I believe the Gram-Charlier expansion can lead to negative prob density for "very" high kurtosis and skewness. I would like to see work on how to improve, get around this.

espen

thanks for that

i second your comment on typos (having just pointed out to my students the three typos amongst the delta and gamma formulas in the lovely ju and zhong paper on analytic american options - well i forgot to mention the third one so one or two of them were scratching their heads a little)

mea culpa, mea culpa

mike

Corrected version now in place.

P