Subject: Question about derivation and normal distribution
From: Julien Martin
Date: Thu, 29 Oct 2009 14:17:52 +0100
After doing some further research I came up with the following:
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(d1,0,1)-K*exp(-r*(T-t))*cdf_normal(d2,0,1)
-diff(C(S,t),t)
which still does not give me the expected result because I would like for
the result be expressed as an expression of d1, d2 and pdf_distrib or
cdf_distrib which is not the case.
For you info I am in reference to the Black and Scholes formula:
http://en.wikipedia.org/wiki/Black%E2%80%93Scholes#Greeks
To L?o: thanks a lot for taking the time to reply. I eventually worked out
that I had to load the distrib package.
Julien.
2009/10/29 Julien Martin <balteo at gmail.com>
> 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.
>>
>
>