heston.hpp

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#pragma once
 
#include <complex>
#include <cstdint>
 
#include "quant/rng.hpp"
 
namespace quant::heston {
 
struct Params {
    double kappa; // mean reversion speed
    double theta; // long-run variance
    double sigma; // vol of vol
    double rho;   // correlation
    double v0;    // initial variance
};
 
struct MarketParams {
    double spot;
    double strike;
    double rate;
    double dividend;
    double time;
};
 
// Analytic European call via Heston characteristic function and Gauss-Laguerre
double call_analytic(const MarketParams& mkt, const Params& h);
 
// Analytic European put from the Heston call and discounted put-call parity
double put_analytic(const MarketParams& mkt, const Params& h);
 
std::complex<double> characteristic_function(double u, const MarketParams& mkt, const Params& h);
 
double implied_vol_call(const MarketParams& mkt, const Params& h);
 
struct McResult {
    double price;
    double std_error;
};
 
struct McParams {
    MarketParams mkt;
    Params h;
    std::uint64_t num_paths;
    std::uint64_t seed;
    int num_steps; // QE time steps
    bool antithetic{true};
    quant::rng::Mode rng{quant::rng::Mode::Counter};
    enum class Scheme { Euler, QE };
    Scheme scheme{Scheme::QE};
};
 
// Andersen QE Monte Carlo pricing of European call
McResult call_qe_mc(const McParams& p);
 
} // namespace quant::heston