diff --git a/matlab/dyn_second_order_solver.m b/matlab/dyn_second_order_solver.m
index f4f1f8519..dd2d2bfb8 100644
--- a/matlab/dyn_second_order_solver.m
+++ b/matlab/dyn_second_order_solver.m
@@ -1,7 +1,7 @@
-function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_BC)
+function dr = dyn_second_order_solver(jacobia,hessian_mat,dr,M_,threads_ABC,threads_BC)
 
 %@info:
-%! @deftypefn {Function File} {@var{dr} =} dyn_second_order_solver (@var{jacobia},@var{hessian},@var{dr},@var{M_},@var{threads_ABC},@var{threads_BC})
+%! @deftypefn {Function File} {@var{dr} =} dyn_second_order_solver (@var{jacobia},@var{hessian_mat},@var{dr},@var{M_},@var{threads_ABC},@var{threads_BC})
 %! @anchor{dyn_second_order_solver}
 %! @sp 1
 %! Computes the second order reduced form of the DSGE model
@@ -11,7 +11,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
 %! @table @ @var
 %! @item jacobia
 %! Matrix containing the Jacobian of the model
-%! @item hessian
+%! @item hessian_mat
 %! Matrix containing the second order derivatives of the model
 %! @item dr
 %! Matlab's structure describing the reduced form solution of the model.
@@ -73,7 +73,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
     kk1 = reshape([1:nk^2],nk,nk);
     kk1 = kk1(kk,kk);
     % reordering second order derivatives
-    hessian = hessian(:,kk1(:));
+    hessian_mat = hessian_mat(:,kk1(:));
 
     zx = zeros(np,np);
     zu=zeros(np,M_.exo_nbr);
@@ -91,7 +91,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
     zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
     [nrzx,nczx] = size(zx);
 
-    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,threads_BC);
+    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian_mat,zx,threads_BC);
     mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
     rhs = -rhs;
 
@@ -118,7 +118,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
     %ghxu
     %rhs
     hu = dr.ghu(nstatic+1:nstatic+nspred,:);
-    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,zu,threads_BC);
+    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian_mat,zx,zu,threads_BC);
     mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
 
     hu1 = [hu;zeros(np-nspred,M_.exo_nbr)];
@@ -136,7 +136,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
 
     %ghuu
     %rhs
-    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zu,threads_BC);
+    [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian_mat,zu,threads_BC);
     mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
 
     [B1, err] = A_times_B_kronecker_C(B*dr.ghxx,hu1,threads_ABC);
@@ -164,7 +164,7 @@ function dr = dyn_second_order_solver(jacobia,hessian,dr,M_,threads_ABC,threads_
     hxx = dr.ghxx(nstatic+[1:nspred],:);
     [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+2,order_var));
     k3 = nnz(M_.lead_lag_incidence(1:M_.maximum_endo_lag+1,:))+(1:M_.nsfwrd)';
-    [B1, err] = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k2a,:),threads_BC);
+    [B1, err] = sparse_hessian_times_B_kronecker_C(hessian_mat(:,kh(k3,k3)),gu(k2a,:),threads_BC);
     mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
     RHS = RHS + jacobia(:,k2)*guu(k2a,:)+B1;
 
diff --git a/matlab/maximize_prior_density.m b/matlab/maximize_prior_density.m
index 131e0422d..72df861a4 100644
--- a/matlab/maximize_prior_density.m
+++ b/matlab/maximize_prior_density.m
@@ -1,4 +1,4 @@
-function [xparams,lpd,hessian] = ...
+function [xparams,lpd,hessian_mat] = ...
     maximize_prior_density(iparams, prior_shape, prior_hyperparameter_1, prior_hyperparameter_2, prior_inf_bound, prior_sup_bound,DynareOptions,DynareModel,BayesInfo,EstimatedParams,DynareResults)
 % Maximizes the logged prior density using Chris Sims' optimization routine.
 % 
@@ -13,7 +13,7 @@ function [xparams,lpd,hessian] = ...
 % OUTPUTS 
 %   xparams       [double]  vector, prior mode.
 %   lpd           [double]  scalar, value of the logged prior density at the mode.
-%   hessian       [double]  matrix, Hessian matrix at the prior mode.
+%   hessian_mat   [double]  matrix, Hessian matrix at the prior mode.
 
 % Copyright (C) 2009-2015 Dynare Team
 %
@@ -32,7 +32,7 @@ function [xparams,lpd,hessian] = ...
 % You should have received a copy of the GNU General Public License
 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
 
-[xparams, lpd, exitflag, hessian]=dynare_minimize_objective('minus_logged_prior_density', ...
+[xparams, lpd, exitflag, hessian_mat]=dynare_minimize_objective('minus_logged_prior_density', ...
                                                   iparams, DynareOptions.mode_compute, DynareOptions, [prior_inf_bound, prior_sup_bound], ...
                                                   BayesInfo.name, BayesInfo, [], ...
                                                   prior_shape, prior_hyperparameter_1, prior_hyperparameter_2, prior_inf_bound, prior_sup_bound, ...
diff --git a/matlab/mode_check.m b/matlab/mode_check.m
index 180ba3592..0f50ca523 100644
--- a/matlab/mode_check.m
+++ b/matlab/mode_check.m
@@ -1,8 +1,8 @@
-function mode_check(fun,x,hessian,DynareDataset,DatasetInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults)
+function mode_check(fun,x,hessian_mat,DynareDataset,DatasetInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults)
 % Checks the estimated ML mode or Posterior mode.
 
 %@info:
-%! @deftypefn {Function File} mode_check (@var{fun}, @var{x}, @var{hessian}, @var{DynareDataset}, @var{DynareOptions}, @var{Model}, @var{EstimatedParameters}, @var{BayesInfo}, @var{DynareResults})
+%! @deftypefn {Function File} mode_check (@var{fun}, @var{x}, @var{hessian_mat}, @var{DynareDataset}, @var{DynareOptions}, @var{Model}, @var{EstimatedParameters}, @var{BayesInfo}, @var{DynareResults})
 %! @anchor{mode_check}
 %! @sp 1
 %! Checks the estimated ML mode or Posterior mode by plotting sections of the likelihood/posterior kernel.
@@ -58,13 +58,13 @@ function mode_check(fun,x,hessian,DynareDataset,DatasetInfo,DynareOptions,Model,
 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
 
 TeX = DynareOptions.TeX;
-if ~isempty(hessian);
-    [ s_min, k ] = min(diag(hessian));
+if ~isempty(hessian_mat);
+    [ s_min, k ] = min(diag(hessian_mat));
 end
 
 fval = feval(fun,x,DynareDataset,DatasetInfo,DynareOptions,Model,EstimatedParameters,BayesInfo,BoundsInfo,DynareResults);
 
-if ~isempty(hessian);
+if ~isempty(hessian_mat);
     skipline()
     disp('MODE CHECK')
     skipline()
diff --git a/matlab/optimize_prior.m b/matlab/optimize_prior.m
index a3595d0f6..d5b5e0ac1 100644
--- a/matlab/optimize_prior.m
+++ b/matlab/optimize_prior.m
@@ -51,7 +51,7 @@ objective_function_penalty_base = minus_logged_prior_density(xinit, BayesInfo.ps
                                BayesInfo.p4,DynareOptions,ModelInfo,EstimationInfo,DynareResults);
 
 % Maximization of the prior density
-[xparams, lpd, hessian] = ...
+[xparams, lpd, hessian_mat] = ...
     maximize_prior_density(xinit, BayesInfo.pshape, ...
                            BayesInfo.p6, ...
                            BayesInfo.p7, ...