Question about derivation and normal distribution



After doing some research I came up with this:

d1=(log(S/K)+(r+sigma^2/2)*(T-t))/(sigma*sqrt(T-t))
d2=d1-(sigma*sqrt(T-t))

C(S,t):=S*cdf_normal(d1)-K*exp(-r*(T-t))*cdf_normal(d2)

-diff(C(S,t),t)

This does not give me the expected result....

Any clue anyone?

Julien.


2009/10/29 Julien Martin <balteo at gmail.com>

> Hello,
> I have the following function:
>
> C(S,t):=S*N(d1)-K*exp(-r*(T-t))*N(d2)
>
> where N(d1) is the normal cumulative distribution with d1 as parameter.
>
> I am trying to use maxima in order to compute a first-order partial
> derivative of the above C(S,t) function as follows:
>
> diff(C(S,t),t)
>
> I don't know how to express the cumulative normal distribution nor how to
> derivate it.
>
> Can anyone please help?
>
> Thanks in advance,
>
> Julien.
>