How to evaluate a string formula within a function?

[David Herzen]

Dear Mata friends,

I have written this simple ready-to-execute code for computing the yield-to-maturity of a two-period coupon-paying bond:

clear
input float(AMOUNTISSUED CF_1 CF_2) double YTM
 100  23  22  .
end

mata
  z=J(1,1,.)
  st_view(z,., "YTM AMOUNTISSUED CF_1 CF_2")
  function s(ytm,amountissued,cf_1,cf_2) {
      
      return((amountissued+cf_2)/ytm^2+cf_1/ytm - amountissued)
  }
 
  for (i=1;i<=rows(z);i++) {
      r=mm_root(YTM=.,&s(),epsilon(1),5-epsilon(1),1e-9,1000,z[i,2],z[i,3],z[i,4])
      YTM-1
      z[i,1]=YTM-1
      
  }
end

However, this code is insufficient for my final purpose: I need to define the function s(.) dynamically for a varying number of cash-flows CF_1 ... CF_N.

Given my limited Mata knowledge, I think that the easiest solution is to write the respective formula as a string using Stata and then to evaluate this formula in the function s(ytm). The code would look like this:

clear
input double YTM str20 formula
. "(100+23)/ytm^2 + 23/ytm - 100"
. "(100+20)/ytm^3 + 20/ytm^2 + 20/ytm- 100"
*. "(100+20)/ytm^N + ... + 20/ytm^2 + 20/ytm- 100"
end

mata
  z=J(1,1,.)
  st_view(z,., "YTM")
  function s(ytm) {
      return(??????????)
  }
 
  for (i=1;i<=rows(z);i++) {
      r=mm_root(YTM=.,&s(),epsilon(1),5-epsilon(1),1e-9,1000)
      YTM-1
      z[i,1]=YTM-1
  }
end

Do you have any suggestions on how to evaluate the string formula "(100+23)/ytm^2 + 23/ytm - 100" using function s(ytm)?

Thank you,
David

[Christophe Kolodziejczyk]

clear
input double YTM str50 formula
. "(100+23)/ytm^2 + 23/ytm - 100"
. "(100+20)/ytm^3 + 20/ytm^2 + 20/ytm- 100"
*. "(100+20)/ytm^N + ... + 20/ytm^2 + 20/ytm- 100"
end

First create the mata functions s1() to s3(). Set the formula in local macros. Then find the adress of theses functions with findexternal().

clear mata
set trace off
set tracedepth 1
forval i = 1/`=_N' {
        local formula `:di formula[`i']'
        mata : function s`i'(ytm) return(`formula');
}

mata : mata describe
scalar Nfunc = _N
mata:
N = st_numscalar("Nfunc")
for (i = 1; i<=N ;i++)
{
        pFunc = findexternal("s"+strofreal(i)+"()")  //  pFunc is successively a pointer to the function s1(), s2(), s3()
        pFunc 
        r=mm_root(YTM=.,pFunc,epsilon(1),5-epsilon(1),1e-9,1000)
        YTM
}
end

Another way is to use a single function s(), which you replace with the correct formula during a loop

set trace off
set tracedepth 1
forval i = 1/`=_N' {
        local formula `:di formula[`i']'
        di "`formula'"

        cap mata mata drop s()
        mata : function s(ytm) return(`formula') 
        mata: r=mm_root(YTM=.,&s(),epsilon(1),5-epsilon(1),1e-9,1000);
        mata: YTM

}

[David Herzen]

Thank you very much, Christophe!

Both approaches help a lot.