Note1- Deriving Black-Scholes
Posted: February 6th, 2002, 3:13 pm
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.
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.