/*
* interpolate the solutions found in r2 onto those found in r1
*/
void interp( int r1, int r2)
{
register int ie1, ie2;
register int i,j, in, fnd;
int *done;
struct tms before, after;
times(&before);
/*initialize the done array*/
done = salloc( int, nn );
for(ie1 = 0; ie1 < nn; ie1++) done[ie1] = FALSE;
/*
This has to be done in a somewhat cludgey fashion,
because the region structure has not been built yet for r1
*/
/*step over all the elements in the first region*/
ie1 = 0;
while( done_tri(ie1) ) {
/*if this triangle is in the region*/
if ( reg_tri(ie1) == r1 ) {
for(i = 0; i < num_vert(ie1); i++) {
in = vert_tri(ie1, i);
if ( done[in] ) continue;
/*now look in the second region for triangles...*/
done[in] = TRUE;
fnd = FALSE;
for(j = 0; !fnd && j < num_tri_reg(r2); j++) {
ie2 = tri_reg(r2,j);
if ( pt_in_tri(cord_arr(pt_nd(in)), ie2 ) ) {
fnd = TRUE;
if ( mode == TWOD ) {
interp_2d(in, ie2);
}
else if (mode == ONED) {
interp_1d(in, ie2);
}
}
}
if ( !fnd ) panic("node not in any triangle");
}
}
next_tri(ie1);
}
free(done);
times(&after);
print_time("total interpolation time", &before, &after);
}
Interpolator_D2 test_Heston_PDE_solution(int CONFIG_sizeDiscretization_y)
{
std::cout << "Model and Product Direction_Parameters" << std::endl;
//! Heston Direction_Parameters
double kappa = Heston_params_kappa;
double theta = Heston_params_theta;
double sigma = Heston_params_sigma;
double rho = Heston_params_rho;
double r = Heston_params_r;
//! Product Direction_Parameters
double K = Option_params_K;
double T = Option_params_T;
//! FD param
double S_max = CONFIG_S_max; // S_max = 2*K is not efficient!
double v_max = CONFIG_v_max;
//! resume: the biggest error is the time!
int sizeDiscretization_t = CONFIG_sizeDiscretization_t + 1;
int sizeDiscretization_x = CONFIG_sizeDiscretization_x + 1;
int sizeDiscretization_y = CONFIG_sizeDiscretization_y + 1;
// //! ma model
//MaModel ma_model(Ma_params_alpha,Ma_params_sigma,Ma_params_rho);
//Ma_Model_discret ma_model_discret(ma_model);
//! Range and discretization
Range range_t(0.0, T);
Range range_x(0.0, S_max);
Range range_y(0.0, v_max);
//! non-uniform
//! direction t
int t_discretization_size = 1;
std::vector<bool> if_nonuniform_t(t_discretization_size);// = OPTIMIZATION_if_nonuniform_sinh_grid_x;
std::vector<bool> if_shift_t(t_discretization_size); // = OPTIMIZATION_if_shfit_grid_x;
std::vector<double> t_nonuniform_center_c(t_discretization_size);// = K;
std::vector<double> t_nonuniform_scale_param_c(t_discretization_size);// = K/5.0;
std::vector<double> t_shifting_center(t_discretization_size); // = K;
if_nonuniform_t[0] = OPTIMIZATION_if_nonuniform_sinh_grid_t;
if_shift_t[0] = OPTIMIZATION_if_shfit_grid_t;
t_nonuniform_center_c[0] = 0.0;
t_nonuniform_scale_param_c[0] = OPTIMIZATION_nonuniform_t_sinh_scale_param; //1.0/500.0;
t_shifting_center[0] = -999999.9;
if(if_fwd_PDE == true)
{
////! add second time
// if_nonuniform_t.push_back(false); // = true;//OPTIMIZATION_if_nonuniform_sinh_grid_t;
//if_shift_t.push_back(false) ; // = OPTIMIZATION_if_shfit_grid_t;
//t_nonuniform_center_c.push_back(0.0); // = 0.0;
//t_nonuniform_scale_param_c.push_back(1.0/50); // = 1.0/25.0;
//t_shifting_center.push_back(-99999.9); // = -999999.9;
}
//! direction x
int x_discretization_size = 1;
std::vector<bool> if_nonuniform_x(x_discretization_size);// = OPTIMIZATION_if_nonuniform_sinh_grid_x;
std::vector<bool> if_shift_x(x_discretization_size); // = OPTIMIZATION_if_shfit_grid_x;
std::vector<double> x_nonuniform_center_c(x_discretization_size);// = K;
std::vector<double> x_nonuniform_scale_param_c(x_discretization_size);// = K/5.0;
std::vector<double> x_shifting_center(x_discretization_size); // = K;
if_nonuniform_x[0] = OPTIMIZATION_if_nonuniform_sinh_grid_x;
if_shift_x[0] = OPTIMIZATION_if_shfit_grid_x;
x_nonuniform_center_c[0] = K;
x_nonuniform_scale_param_c[0] = K/5.0;
x_shifting_center[0] = K;
if(if_fwd_PDE == true)
{
x_nonuniform_center_c[0] = fwd_PDE_S0;
x_nonuniform_scale_param_c[0] = OPTIMIZATION_nonuniform_x_sinh_scale_param;
x_shifting_center[0] = fwd_PDE_S0;
}
//! direction y
int y_discretization_size = 1;
std::vector<bool> if_nonuniform_y(y_discretization_size);
std::vector<bool> if_shift_y(y_discretization_size);
std::vector<double> y_nonuniform_center_c(y_discretization_size);
std::vector<double> y_nonuniform_scale_param_c(y_discretization_size);
std::vector<double> y_shifting_center(y_discretization_size);
if_nonuniform_y[0] = OPTIMIZATION_if_nonuniform_sinh_grid_y;
if_shift_y[0] = OPTIMIZATION_if_shfit_grid_y; //! for Fwd PDE
y_nonuniform_center_c[0] = 0.0;
y_nonuniform_scale_param_c[0] = OPTIMIZATION_nonuniform_y_sinh_scale_param; // V_max/500 is the experienced choice!
y_shifting_center[0] = -99999.9;
if(if_fwd_PDE == true)
{
//! first dimension:
if_nonuniform_y[0] = OPTIMIZATION_if_nonuniform_sinh_grid_y; // OPTIMIZATION_if_nonuniform_sinh_grid_y;
if_shift_y[0] = OPTIMIZATION_if_shfit_grid_y; // OPTIMIZATION_if_shfit_grid_y; //! for Fwd PDE
y_nonuniform_center_c[0] = 0.0;//Heston_params_theta;
y_nonuniform_scale_param_c[0] = OPTIMIZATION_nonuniform_y_sinh_scale_param; // OPTIMIZATION_nonuniform_y_sinh_scale_param; //1.0/10000.0; // V_max/500 is the experienced choice!
y_shifting_center[0] = fwd_PDE_v0;
////! second dimension:
//if_nonuniform_y.push_back(false);
//if_shift_y.push_back(true);
//y_nonuniform_center_c.push_back(fwd_PDE_v0);
//y_nonuniform_scale_param_c.push_back(1.0/*OPTIMIZATION_nonuniform_y_sinh_scale_param*/);
//y_shifting_center.push_back(fwd_PDE_v0);
////! third
//if_nonuniform_y.push_back(false);
//if_shift_y.push_back(true);
//y_nonuniform_center_c.push_back(Heston_params_theta);
//y_nonuniform_scale_param_c.push_back(1.0/5000.0);
//y_shifting_center.push_back(fwd_PDE_v0);
}
Discretization discret( range_t, sizeDiscretization_t,
range_x, sizeDiscretization_x,
range_y, sizeDiscretization_y,
if_nonuniform_t, t_nonuniform_center_c, t_nonuniform_scale_param_c,
if_shift_t, t_shifting_center,
if_nonuniform_x, x_nonuniform_center_c, x_nonuniform_scale_param_c,
if_shift_x, x_shifting_center,
if_nonuniform_y, y_nonuniform_center_c, y_nonuniform_scale_param_c,
if_shift_y, y_shifting_center);
//! Heston Model
HestonModel model(r,sigma,kappa,theta,rho);
//Heston_Model_discret heston_model_discret(model);
//! Heston discret Model
PDE_Model_Heston heston_model_discret(model,discret);
//! Term Structure, Payoff && Boundary Condition
//! Don't want to use this one, it will make error in the code !
//! Because Heston model calls directly r() of Heston model :)
Term_Structure* cts = NULL; //new Const_Term_Structure(-999999);
PayoffYuan* payoff = new Put(K);
//! Backward PDE
//BoundaryCondition_Heston_Put bc(cts, payoff, model, discret);
//! Forward PDE
BoundaryCondition_D2_density_CONSTPTR bc (new BoundaryCondition_D2_density (model, discret,fwd_PDE_S0,fwd_PDE_v0, cts, payoff ));
//! --------------------------------------------------
//!
//! Test PDE solver
//!
//! ---------------------------------------------------
//! new Scheme class
Scheme_ADI* scheme_new_ptr = NULL;
if(scheme_type ==1)
{
scheme_new_ptr= new Scheme_Yanenko(
discret,
heston_model_discret,
bc
);
}
else if(scheme_type ==2)
{
scheme_new_ptr = new Scheme_Douglas(
discret,
heston_model_discret,
bc,
scheme_douglas_theta
);
}
else if (scheme_type == 3)
{
scheme_new_ptr = new Scheme_CS(
discret,
heston_model_discret,
bc,
scheme_douglas_theta,
scheme_douglas_lambda
);
}
else if(scheme_type == 4)
{
scheme_new_ptr = new Scheme_MCS(
discret,
heston_model_discret,
bc,
scheme_douglas_theta,
scheme_douglas_lambda
);
}
else if(scheme_type == 5)
{
scheme_new_ptr = new Scheme_HV(
discret,
heston_model_discret,
bc,
scheme_douglas_theta
);
}
else
{
throw ("Error in Test_PDE.cpp, scheme_type does not take valid value");
}
PDE_ADI_Solver pde_solver(*scheme_new_ptr);
//! --------------------------------------------------
//!
//! Test PDE solver extrapolation
//!
//! ---------------------------------------------------
//PDE_ADI_Extrapolation_Solver pde_extrapolation_solver( scheme_type,
// discret,
// heston_model_discret,
// // --- For constructing: stupid bc (Bad Bad design !!!)
// cts,
// payoff,
// model,
// // ----
// scheme_douglas_theta,
// scheme_douglas_lambda);
clock_t t1 = clock();
//if(DEBUG_test_PDE_solver_extrapolation == true)
//{
// pde_extrapolation_solver.solve_PDE();
//}
//else
{
pde_solver.solve_PDE();
}
clock_t t2 = clock();
cout << "time = " << (double)(t2-t1)/CLOCKS_PER_SEC << " seconds"<< endl;
////! Fwd PDE
////! find initial dirac point
//int dirac_x_index = -1;
//int dirac_y_index = -1;
//vector<double> discret_x_tilde = discret.get_discret_x_tilde();
//vector<double> discret_y_tilde = discret.get_discret_y_tilde();
//for(unsigned int i=0; i<discret_x_tilde.size(); ++i)
//{
// double x = discret_x_tilde[i];
// if(fabs(x-fwd_PDE_S0)<0.000000001)
// {
// dirac_x_index = i;
// break;
// }
//}
//for(unsigned int j=0; j<discret_y_tilde.size(); ++j)
//{
// double y = discret_y_tilde[j];
// if(fabs(y-fwd_PDE_v0)<0.000000001)
// {
// dirac_y_index = j;
// break;
// }
//}
//
//double inital_proba = 1.0/4
// *( discret.get_delta_x(dirac_x_index)+discret.get_delta_x(dirac_x_index+1) )
// *( discret.get_delta_y(dirac_y_index)+discret.get_delta_y(dirac_y_index+1) );
//cout << "inital_proba = " << inital_proba << endl;
double inital_proba = 1.0;
//! check sum of probability:
Matrix Fwd_PDE_result (pde_solver.get_result());
Fwd_PDE_result /= inital_proba;
double sum_proba = 0.0;
double sum_proba_positive = 0.0;
double sum_proba_negative = 0.0;
for( int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
int index_i = i+1;
for( int j=0; j<discret.get_sizeDiscret_y_tilde(); ++j)
{
int index_j = j+1;
double density = Fwd_PDE_result[index_i][index_j]; // then it is the density
double coeff = 1.0/4
*( discret.get_delta_x(i)+discret.get_delta_x(i+1) )
*( discret.get_delta_y(j)+discret.get_delta_y(j+1) );
double proba = coeff*density;
if(density>0.0)
{
sum_proba_positive += coeff*density;
}
else
{
sum_proba_negative += coeff*density;
}
}
}
sum_proba = sum_proba_positive + sum_proba_negative;
cout << " ---- |||| ---- |||| Sum_Proba = " << sum_proba << endl; //<< ", sum_proba_positive = " << sum_proba_positive << " + " << "sum_proba_negative = " << sum_proba_negative << endl;
cout << " ---- |||| ---- |||| Sum_Proba_positive = " << sum_proba_positive << endl;
cout << " ---- |||| ---- |||| Sum_Proba_negative = " << sum_proba_negative << endl;
cout << " ---- |||| ---- |||| Sum_total_error = " << fabs(sum_proba_positive - 1) + fabs(sum_proba_negative) << endl;
//! analytical price
int num_K = 17;
double step = 0.05;
//double K_start = Option_params_K*(num_K-1)/
vector<double> v_K(num_K);
vector<double> v_analytical_price(num_K);
cout << "strike vector: "<< endl;
cout << Option_params_K << endl;
v_K[0] = Option_params_K;
for(unsigned int i=1; i<v_K.size()-1; i+=2)
{
v_K[i] = Option_params_K *(1+i*step);
v_K[i+1] = Option_params_K *(1-i*step);
cout << v_K[i] << endl;
cout << v_K[i+1] << endl;
}
for(unsigned int i=0; i<v_K.size(); ++i)
{
Heston_analytical_pricer pricer_ana(v_K[i]);
v_analytical_price[i] = pricer_ana.heston_put(fwd_PDE_S0,fwd_PDE_v0, 1024*10);
}
vector<double> v_numerical_price(num_K);
//! first numerical integration price
for(unsigned int kk=0; kk<v_K.size()-1; ++kk)
{
double KK = v_K[kk];
double sum_price = 0.0;
double sum_price_positive = 0.0;
double sum_price_negative = 0.0;
for( int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
int index_i = i+1;
double payoff = 1;
double x = discret.get_discret_x(index_i);
if(x<KK)
payoff = KK - x;
else
payoff = 0.0;
for( int j=0; j<discret.get_sizeDiscret_y_tilde(); ++j)
{
int index_j = j+1;
double density = Fwd_PDE_result[index_i][index_j]; // then it is the density
double coeff = 1.0/4
*( discret.get_delta_x(i)+discret.get_delta_x(i+1) )
*( discret.get_delta_y(j)+discret.get_delta_y(j+1) );
double proba = coeff*density;
if(density>0.0)
{
sum_price_positive += coeff*density*payoff;
}
else
{
sum_price_negative += coeff*density*payoff;
}
}
}
sum_price_positive *= exp(-Option_params_T*Heston_params_r);
sum_price_negative *= exp(-Option_params_T*Heston_params_r);
sum_price = sum_price_positive + sum_price_negative;
v_numerical_price[kk] = sum_price;
cout << "1st numerical price = " << sum_price << endl;
//cout << "price_numerical_positive = " << sum_price_positive << endl;
//cout << "price_numerical_negative = " << sum_price_negative << endl;
//!second numerical integration price
vector<double> x_grid(discret.get_discret_x_tilde());
vector<double> y_grid(discret.get_discret_y_tilde());
vector<double> x_value(discret.get_sizeDiscret_x_tilde(),0.0);
vector<double> y_value(discret.get_sizeDiscret_y_tilde(),0.0);
for(int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
int index_i = i+1;
double payoff = 1;
//double x = discret.get_discret_x(index_i);
//if(x<KK)
// payoff = KK - x;
//else
// payoff = 0.0;
for(int j=0; j<discret.get_sizeDiscret_y_tilde(); ++j)
{
int index_j = j+1;
y_value[j] = Fwd_PDE_result[index_i][index_j];
}
Interpolator interp_y(y_grid,y_value);
x_value[i] = interp_y.calculate_integral_approximation()*payoff;
}
Interpolator interp_x(x_grid,x_value);
double second_analytical_price = interp_x.calculate_integral_approximation();
//second_analytical_price *= exp(-Option_params_T*Heston_params_r);
cout << "2nd numerical price = " << second_analytical_price << endl;
//! third numerical integration price
double third_sum_price = 0.0;
vector<double> v_sum_x(discret.get_sizeDiscret_x_tilde(),0.0);
vector<double> v_sum_x_positive(discret.get_sizeDiscret_x_tilde(),0.0);
vector<double> v_sum_x_negative(discret.get_sizeDiscret_x_tilde(),0.0);
for( int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
int index_i = i+1;
double payoff = 1;
//double x = discret.get_discret_x(index_i);
//if(x<KK)
// payoff = KK - x;
//else
// payoff = 0.0;
double sum_x = 0.0;
double sum_x_positive = 0.0;
double sum_x_negative = 0.0;
for( int j=0; j<discret.get_sizeDiscret_y_tilde(); ++j)
{
int index_j = j+1;
double density = Fwd_PDE_result[index_i][index_j]; // then it is the density
double coeff = ( discret.get_delta_y(j)+discret.get_delta_y(j+1) )/2;
double proba = coeff*density;
if(density>0.0)
{
sum_x_positive += coeff*density*payoff;
}
else
{
sum_x_negative += coeff*density*payoff;
}
sum_x = sum_x_positive + sum_x_negative;
}
v_sum_x_positive[i] = sum_x_positive;
v_sum_x_negative[i] = sum_x_negative;
v_sum_x[i] = sum_x;
}
double hehe = 0.0;
for( int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
double interval = ( discret.get_delta_x(i)+discret.get_delta_x(i+1) )/2.0;
hehe += v_sum_x[i]*interval;
}
cout << "3rd numerical price = " << hehe << endl;
}
Interpolator_D2 interp_2d(discret.get_discret_x(), discret.get_discret_y(), Fwd_PDE_result);
////sum_price_positive *= exp(-Option_params_T*Heston_params_r);
////sum_price_negative *= exp(-Option_params_T*Heston_params_r);
//sum_price = sum_price_positive + sum_price_negative;
//cout << "price_numerical = " << sum_price << endl;
//cout << "price_numerical_positive = " << sum_price_positive << endl;
//cout << "price_numerical_negative = " << sum_price_negative << endl;
//! Print one price
if(DEBUG_PDE_error_print_to_screen == true)
{
cout.precision(15);
int S_index = 25;
int v_index = 10;
double S_check = discret.get_discret_x(S_index);
double v_check = discret.get_discret_y(v_index);
//Matrix PDE_result = pde_solver.get_result();
Matrix PDE_result(1,1,0);
//if(DEBUG_test_PDE_solver_extrapolation == true)
//{
// PDE_result = pde_extrapolation_solver.get_result();
//}
//else
{
PDE_result = pde_solver.get_result();
}
Heston_analytical_pricer analytical_pricer;
vector<double> discret_x;
discret_x.push_back(S_check);
cout << "PDE's price for So=" << S_check << ", v=" << v_check << " = " << PDE_result[S_index][v_index] << endl;
vector<double> discret_y;
discret_y.push_back(v_check);
Matrix analytical_price = analytical_pricer.heston_put_v(discret_x,discret_y, 1024*100);
cout.precision(15);
cout << "analytical formula's price = " << analytical_price[0][0]<< endl;
}
if (DEBUG_PDE_error_print_to_file == true)
{
std::stringstream ss;
ss << CONFIG_sizeDiscretization_y;
string s = ss.str();
std::string PDE_error_output_file_name = DEBUG_output_path + s + "PDE_error.csv";
//! get PDE result
//Matrix PDE_result = pde_solver.get_result();
//Matrix PDE_result(1,1,0);
//if(DEBUG_test_PDE_solver_extrapolation == true)
//{
// PDE_result = pde_extrapolation_solver.get_result();
//}
//else
//{
// PDE_result = pde_solver.get_result();
//}
Matrix PDE_result = Fwd_PDE_result;
//! get analytical result
Heston_analytical_pricer analytical_pricer;
vector<double> discret_x(discret.get_discret_x());
vector<double> discret_y(discret.get_discret_y());
//! Backward PDE
//double Error_S_min = 0.5 * Option_params_K;
//double Error_S_max = 1.5 * Option_params_K;
//double Error_v_min = 0;
//double Error_v_max = 1.0;
//! Fwd PDE
double Error_S_min = 0;
double Error_S_max = S_max; // 1.5 * Option_params_K;
double Error_v_min = 0;
double Error_v_max = v_max; //1.0;
vector<double> x_vector_value; //! For analytical price
vector<int> x_vector_index;
vector<double> y_vector_value; //! For PDE price (index)
vector<int> y_vector_index;
for( int i=0; i<discret.get_sizeDiscret_x_tilde(); ++i)
{
double x = discret_x[i];
if(x>=Error_S_min-0.000000001 && x <= Error_S_max+0.000000001)
{
x_vector_value.push_back(x);
x_vector_index.push_back(i);
}
}
for(unsigned int i=0; i<discret_y.size(); ++i)
{
double y = discret_y[i];
if(y>=Error_v_min-0.000000001 && y <= Error_v_max+0.000000001)
{
y_vector_value.push_back(y);
y_vector_index.push_back(i);
}
}
Matrix analytical_price(1,1,0.0);
if(DEBUG_PDE_test_PDE_vs_analytical == true)
{
analytical_price = analytical_pricer.heston_put_v(x_vector_value,y_vector_value);
}
Matrix PDE_error((int)x_vector_value.size(), (int)y_vector_value.size(),-9999.0);
for(unsigned int i=0; i<x_vector_value.size(); ++i)
{
for(unsigned int j=0; j<y_vector_value.size(); ++j)
{
if(DEBUG_PDE_test_PDE_vs_analytical == true)
{
PDE_error[i][j] = PDE_result[x_vector_index[i]][y_vector_index[j]] - analytical_price [i][j];
}
else if (DEBUG_PDE_test_only_PDE == true)
{
PDE_error[i][j] = PDE_result[i][j];
}
}
}
print_result(PDE_error_output_file_name , x_vector_value, y_vector_value, PDE_error);
//! find max error
if(DEBUG_PDE_test_PDE_vs_analytical == true)
{
double max_error_value = 0.0;
int max_error_index_S = 0;
int max_error_index_v = 0;
for(unsigned int i=0; i<x_vector_value.size(); ++i)
{
for(unsigned int j=0; j<y_vector_value.size(); ++j)
{
if(abs(PDE_error[i][j]) > abs(max_error_value))
{
max_error_value = PDE_error[i][j];
max_error_index_S = i;
max_error_index_v = j;
}
}
}
//!!!!! I donot know why but Error !!!! -- Max error = 17
cout << "---- ---- ---- ---- Max_error_value is at (" << x_vector_value[max_error_index_S]<< ","<< y_vector_value[max_error_index_v] << ") = " << max_error_value << endl;
}
}
for(unsigned int i=0; i<v_K.size(); ++i)
{
cout << "v_K[" << i << "] = "<< v_K[i] << " 's price: " << v_analytical_price[i] << " ~ " << v_numerical_price[i] << endl;
}
delete cts;
delete payoff;
//delete scheme_ptr;
delete scheme_new_ptr;
return interp_2d;
}