Solvenl - Optimize for 2 unknown variables (in Mata)

[Alexander Hösle]

Hi all,
i try to solve the Black-Scholes-Merton formula for two unknwons: Asset Value & Asset Volatility.

My basic code is from this topic:
https://www.statalist.org/forums/for...atility-merton

but i want to solve it with "solvenl"

I have problems with the syntax of solvenl. Espacially i don't know how i can change my code the Avalue & Avol change to set lnf to zero (or near zero).

My error message is:

Solver(): 3001 expected 2 arguments but received 4
solvenl__calluser_2(): - function returned error
solvenl__functioneval(): - function returned error
solvenl_solve__broydenpowell(): - function returned error
_solvenl_solve(): - function returned error
solvenl_solve(): - function returned error
<istmt>: - function returned error


With my code

clear*
set obs 2
gen ev = 100 
replace ev = 120 in 2
gen evola = .15 
replace evola = .13 in 2
gen debt = 50 
replace debt = 70 in 2
gen r = .05 
replace r = .045 in 2
gen t = 1
gen Avalue = .
gen avol = .

mata
mata clear
j=1
 T = st_data(j,"t")
 sqrtT = sqrt(T)
 rf= st_data(j,"r")
 F = st_data(j, "debt")
 E = st_data(j, "ev")
 Evol = st_data(j, "evola")
 Avol = Evol*(E/(E+F))
 Avalue = (E + F)
 //A = (Avalue, Avol)
 //c = (sqrtT, rf, E, Evol, F)

        void function Solver(Avol, Avalue) ///
  
  {

                                //d1=(ln(Avalue/F)+(rf+0.5*(Avol)^2)*(sqrtT)^2)/(Avol*sqrtT)
                                //d2=d1-Avol*sqrtT
                                //E_calc=Avalue*normal(d1)- exp(-rf*(sqrtT)^2)*F*normal(d2)
                                //Evol_calc=(Avalue/E_calc)*normal(d1)*Avol
                                //lnf =(E_calc/E-1)^2 + (Evol_calc/Evol-1)^2
                                
                                lnf=    (Avalue*normal((ln(Avalue/F)+(rf+0.5*(Avol)^2)*(sqrtT)^2)/(Avol*sqrtT))- ///
                                        exp(-rf*(sqrtT)^2)*F* ///
                                        normal((ln(Avalue/F)+(rf+0.5*(Avol)^2)*(sqrtT)^2)/(Avol*sqrtT)-Avol*sqrtT)-E-1)^2+ ///
                                        ((Avalue/E_calc)*normal((ln(Avalue/F)+(rf+0.5*(Avol)^2)*(sqrtT)^2)/(Avol*sqrtT))*Avol-Evol-1)^2
                                
                }


                        S = solvenl_init()
                        solvenl_init_argument(S,1,Avalue)
                        solvenl_init_argument(S,2,Avol)
                        solvenl_init_evaluator(S, &Solver())
                        
                        solvenl_init_numeq(S, 1)
                        solvenl_init_type(S, "zero")
                        
                        solvenl_init_conv_maxiter(S, 100)
                           ERR=solvenl_result_error_code(S)
                        //solvenl_init_iter_log(S,"off)
                        //_solvenl_solve(S)
                        //solvenl_dump(S)
                        A = solvenl_solve(S)

                        st_store(j, "Avalue", A[1])
                        st_store(j, "avol", A[2])

                        
    
end

Can someone please shortly explain which arguments i should use and how i can change the function to min lnf?
Thank you very much!

I got my solvenl-knowlege from
https://www.statalist.org/forums/for...venl-arguments
and
https://www.stata.com/help13.cgi?mf_solvenl
althoug i use Stata 14.