$ONEMPTY

SETS
   RFD                / 1*1 /
   I                  / 1*1 /

PARAMETER T_DELTA(RFD)
/
1     -64452.739441
/
;


PARAMETER TOLERANCE(RFD)
/
1     0.100000
/
;


TABLE DELTA(RFD,I)
$ONDELIM
RFD,1
1,-200.235084
$OFFDELIM
;

display delta;

VARIABLES
   X(I)
   D_HDG
   TARGET;

* -------- EQUATION SECTION ------------------------------------------

EQUATIONS
   E_DHEDGE
   E_HEDGE
   E_DTOLL(RFD)
   E_DTOLU(RFD);

E_DHEDGE..
  SUM(RFD,SQR(SUM(I,X(I)*DELTA(RFD,I)) - T_DELTA(RFD))) =E= D_HDG;

E_HEDGE.. 
  D_HDG =E= TARGET;

E_DTOLL(RFD)..
  SUM(I,X(I)*DELTA(RFD,I)) =G= 
    T_DELTA(RFD) - TOLERANCE (RFD) * ABS (T_DELTA(RFD));

E_DTOLU(RFD)..
  SUM(I,X(I)*DELTA(RFD,I)) =L= 
    T_DELTA(RFD) + TOLERANCE (RFD) * ABS (T_DELTA(RFD));

* -------- MODEL SECTION ------------------------------------------

MODEL Hedge
/
   E_DHEDGE,
   E_HEDGE,
   E_DTOLL,
   E_DTOLU
/;

* option nlp = minos5;

* SOLVE Hedge MINIMIZING TARGET USING NLP;

e_dhedge.scale = 1e6;
d_hdg.scale = 1e6;
Hedge.scaleopt = 0;

SOLVE Hedge MINIMIZING D_HDG USING NLP;