[Maxima] Twofold problem with Maxima: derivative of cdf_normal and expressing result as an expression of a var...
raymond.toy at stericsson.com
Thu Oct 29 12:07:20 CDT 2009
Julien Martin wrote:
> I am trying to use Maxima in order to compute a partial derivative of
> the C(S,t) function below
> C(S,t):=S*cdf_normal(d1,0,1) - K*exp(-r*(T-t))*cdf_normal(d2,0,1)
> For you information I am in reference to the Black and Scholes
> formula: http://en.wikipedia.org/wiki/Black%E2%80%93Scholes#Greeks and
> I am trying to compute the Theta.
> The problem is that this does not give me the expected result because
> I would like for the result be expressed as an expression of d1, d2.
> How can I achieve that??
> Morevoer, I should get a pdf_distrib (derivative of cdf_distrib)
> somewhere in the result.
Why do you think you should get a pdf_distrib in the result? The
derivative of the cdf_normal is easily expressed as an exponential
function, and that's what maxima does.
Perhaps, you want something like:
C(S,t):=S*cdf_normal(nd1,0,1) - K*exp(-r*(T-t))*cdf_normal(nd2,0,1)
depends(nd1, t, nd2, t)
This will give you an expression in term of nd1, nd2, and the
derivatives of nd1 and nd2.
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