Beginner really needs help with Maxima's basic concepts

Thanks a lot to you too Eric!

I am also experiencing difficulties with the syntax of your:
*s:solve([F-f,P-p],[F,u,d]);
ss:s[2][1];

*Can you please describe in English what the above two line mean - if and
when you have the time to do so of course :-)

Thanks in advance,

Julien.

2009/11/11 reyssat <eric.reyssat at math.unicaen.fr>

> Julien Martin a ?crit :
>
>> Hello,
>>
>> I am working on the binomial model and my example is based on that but
>> really my question relates to Maxima's basic concepts.
>>
>> Here is my example:
>>
>> I have %Delta and p defined as follows:
>>
>> *%Delta:(fu-fd)/(S0*u-S0*d); (1)*
>>
>> *p:(exp(r*T)-d)/(u-d); (2)*
>>
>> I need to have the following expression (3) simplified by replacing the
>> %Delta with the expression given above in (1) and expressed in terms of p as
>> defined above in (2)...
>>
>> *f:S0*%Delta*(1-u*exp(-r*T))+fu*exp(-r*T); (3)*
>>
>> ...so that I would ideally get this:
>>
>> *f:exp(-r*T)*(p*fu + (1-p) * fd); (4)*
>>
>> Is this possible? Can someone please help?
>>
>> Julien.
>> ------------------------------------------------------------------------
>>
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>>
>>
> Hello,
> since you want to eliminate u and d in f, and express it in terms of the
> other parameters only, you can solve in terms of f,u,d :
>
> (%i2) %Delta:(fu-fd)/(S0*u-S0*d);
> (%o2) (fu-fd)/(u*S0-d*S0)
>
> (%i3) p:(exp(r*T)-d)/(u-d);
> (%o3) (%e^(r*T)-d)/(u-d)
>
> (%i4) f:S0*%Delta*(1-u*exp(-r*T))+fu*exp(-r*T);
> (%o4) (fu-fd)*S0*(1-u*%e^-(r*T))/(u*S0-d*S0)+fu*%e^-(r*T)
>
> (%i5) s:solve([F-f,P-p],[F,u,d]);  ss:s[2][1];
> (%o5) [[F = %r1,u = %e^(r*T),d = %e^(r*T)],
>      [F = ((fu-fd)*P+fd)*%e^-(r*T),u = %r2,d = -(%e^(r*T)-%r2*P)/(P-1)]]
> (%o6) F = ((fu-fd)*P+fd)*%e^-(r*T)
>
> which is almost your expected answer (need to collect coefficient of fd).
>
> Eric
>