mc.hpp

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#pragma once
 
#include <cstdint>
#include <optional>
#include <random>
#include <vector>
 
#include "quant/rng.hpp"
#include "quant/term_structures.hpp"
 
namespace quant::mc {
 
struct McParams {
    double spot;             // S0
    double strike;           // K
    double rate;             // r
    double dividend;         // q
    double vol;              // sigma
    double time;             // T
    std::uint64_t num_paths; // number of primary paths (antithetic doubles effective)
    std::uint64_t seed;      // RNG seed
    bool antithetic{true};
    bool control_variate{true}; // control variate on discounted S_T vs E[S_T]
    quant::rng::Mode rng{quant::rng::Mode::Counter};
    enum class Qmc { None, Sobol, SobolScrambled };
    enum class Bridge { None, BrownianBridge };
    Qmc qmc{Qmc::None};
    Bridge bridge{Bridge::None};
    int num_steps{1};
    // Optional piecewise-constant schedules; when set, override scalar rate/div/vol
    std::optional<quant::PiecewiseConstant> rate_schedule{};
    std::optional<quant::PiecewiseConstant> dividend_schedule{};
    std::optional<quant::PiecewiseConstant> vol_schedule{};
};
 
struct McStatistic {
    double value;     // sample mean
    double std_error; // standard error of the estimate
    double ci_low;    // 95% confidence interval lower bound
    double ci_high;   // 95% confidence interval upper bound
};
 
struct McResult {
    McStatistic estimate; // price estimate and uncertainty
};
 
McResult price_european_call(const McParams& p);
 
struct GreeksResult {
    McStatistic delta;       // pathwise
    McStatistic vega;        // pathwise
    McStatistic gamma_lrm;   // likelihood-ratio
    McStatistic gamma_mixed; // mixed (pathwise × LR)
    McStatistic theta;       // finite-difference in time with common RNG
};
 
GreeksResult greeks_european_call(const McParams& p);
 
} // namespace quant::mc