grid_utils.hpp

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#pragma once
 
#include <vector>
 
#include "quant/barrier.hpp"
 
namespace quant::grid_utils {
 
struct SpaceGrid {
    std::vector<double> coordinate; // Differencing coordinate (S or log S)
    std::vector<double> spot;       // Underlying spot values corresponding to coordinate nodes
};
 
// Hyperbolic-tangent stretch map with anchor in [0,1].
double stretch_map(double xi, double anchor, double stretch);
 
struct StretchedGridParams {
    int nodes;      // number of grid points (>= 1)
    double lower;   // lower bound in spot space (S-space)
    double upper;   // upper bound in spot space (S-space)
    double anchor;  // anchor spot value to focus grid density (typically strike)
    double stretch; // tanh stretch parameter (0 => uniform)
    bool log_space; // when true, coordinate is ln(S)
};
 
SpaceGrid build_space_grid(const StretchedGridParams& params);
 
struct DiffusionCoefficients {
    double sigma;    // instantaneous volatility
    double rate;     // risk-free rate
    double dividend; // dividend yield
    bool log_space;  // match grid coordinate system
};
 
struct OperatorWorkspace {
    std::vector<double> lower;
    std::vector<double> diag;
    std::vector<double> upper;
    std::vector<double> rhs;
};
 
// Assemble interior tridiagonal coefficients for a backward Euler/Crank-Nicolson step.
// "theta" = 1 corresponds to fully implicit, 0.5 => Crank-Nicolson.
void assemble_operator(const SpaceGrid& grid, const DiffusionCoefficients& coeffs, double dt, double theta,
                       const std::vector<double>& v_curr, OperatorWorkspace& op);
 
struct PayoffBoundaryParams {
    ::quant::OptionType type;
    double strike;
    double rate;
    double dividend;
    double tau; // remaining time to maturity (years)
};
 
double dirichlet_boundary(const PayoffBoundaryParams& params, double spot, bool is_lower);
 
} // namespace quant::grid_utils