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double Option_Price_Family::compute_delta_before_expectation(const double current_underlying_value, const double s, const double t, const double sigma_s_t,const Option_Price_Family& next_option_price_family) {
Price_and_Trajectory pat;
double result;
double tmp ;
double tmp_phi = 0.;
double tmp_one = 0.;
double rmp ;
double rmp_phi = 0.;
double rmp_one = 0.;
double diff_x_alpha = 0.;
double indicatrice = 0.;
double price = 0.;
/// keep track of recomputations when result_one ~ 0
if (S_use_localization) {
for (int j=0; j<Option_Price_Family::S_SIMUL__M; j++) {
pat = next_option_price_family.m_prices_and_trajectories[j];
diff_x_alpha = pat.m_last_underlying_value - current_underlying_value;
tmp = ( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t ) / (pat.m_last_underlying_value* sigma_s_t);
if (S_use_reverse_formula) {
tmp *= S_F(- diff_x_alpha)- S_H(- diff_x_alpha);
tmp += S_f(- diff_x_alpha);
} else {
tmp *= S_H(diff_x_alpha)- S_F(diff_x_alpha);
tmp += S_f(diff_x_alpha);
}
tmp_one += tmp;
tmp_phi += tmp * pat.m_option_price;
//rmp = ( pow( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t, 2 ) +t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t - s*t*(t-s) )/ (pow(pat.m_last_underlying_value,2)* sigma_s_t);
rmp = ( pow( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t, 2 ) +(t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t)*sigma_s_t - s*t*(t-s) )/ (pow(pat.m_last_underlying_value,2)* pow(sigma_s_t,2));
if (S_use_reverse_formula) {
rmp *= (S_F( diff_x_alpha)- S_H( diff_x_alpha));
rmp -= (S_f( diff_x_alpha)*( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t ) / pat.m_last_underlying_value);
} else {
rmp *= S_H(diff_x_alpha) - S_F(diff_x_alpha);
rmp -= S_f(diff_x_alpha)*( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t ) / (pat.m_last_underlying_value*sigma_s_t);
}
rmp_one += rmp;
rmp_phi += rmp * pat.m_option_price;
}
} else {
for (int j=0; j<Option_Price_Family::S_SIMUL__M; j++) {
pat = next_option_price_family.m_prices_and_trajectories[j];
tmp = ( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t ) / pat.m_last_underlying_value;
diff_x_alpha = pat.m_last_underlying_value - current_underlying_value;
if (S_use_reverse_formula) {
tmp *= - S_H(- diff_x_alpha);
} else {
tmp *= S_H(diff_x_alpha);
}
tmp_one += tmp;
tmp_phi += tmp * pat.m_option_price;
}
}
tmp_one /= Option_Price_Family::S_SIMUL__M;
tmp_phi /= Option_Price_Family::S_SIMUL__M;
rmp_one /= Option_Price_Family::S_SIMUL__M;
rmp_phi /= Option_Price_Family::S_SIMUL__M;
price = std::max(S_payoff(current_underlying_value),S_one_step_discount*tmp_phi/tmp_one);
indicatrice = (price<S_payoff(current_underlying_value))?1:0;
//return S_one_step_discount*(tmp_phi*rmp_one - rmp_phi*tmp_one)/(pow(rmp_one,2));
//return S_one_step_discount*(rmp_phi*tmp_one - tmp_phi*rmp_one)/(pow(tmp_one,2));
//return ( pow( t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t, 2 ) +(t * pat.m_last_brownian - s * pat.m_current_brownian + sigma_s_t)*sigma_s_t - s*t*(t-s) )/ (pow(pat.m_last_underlying_value,2)* sigma_s_t);
//double square = tmp_one*tmp_one;
result = (double)(rmp_phi*tmp_one - tmp_phi*rmp_one)/((double)tmp_one * (double)tmp_one);
//return result/tmp_one;
//return (tmp_one/pow(tmp_one,2));
return result;
}
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