70 lines
2.1 KiB
C++
70 lines
2.1 KiB
C++
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/**
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* @file BlackScholesClosedFormEngine.cpp
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* @brief Black–Scholes closed-form pricing (calls, puts, cash-or-nothing digital).
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*/
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#include "BlackScholesClosedFormEngine.hpp"
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#include "Instrument.hpp"
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#include "Payoff.hpp"
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#include <cmath>
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#include <stdexcept>
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namespace {
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double norm_cdf(double x) {
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return 0.5 * (1.0 + std::erf(x / std::sqrt(2.0)));
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}
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} // namespace
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double BlackScholesClosedFormEngine::calculate(const Instrument &instrument) const {
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if (instrument.exerciseType() != Exercise::Type::European) {
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throw std::invalid_argument("BlackScholesClosedFormEngine: European exercise only");
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}
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const double T = instrument.maturity();
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const MarketData &md = process_->data();
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const double S = md.spot();
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double K = instrument.payoff().strike();
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const PayoffKind pk = instrument.payoff().kind();
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if (T <= 0.0) {
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return instrument.payoff()(S);
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}
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const double r = md.yield_curve().zeroRate(T);
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const double sigma = md.volatility_surface().sigma(K, T);
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if (sigma <= 0.0) {
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throw std::invalid_argument("BlackScholesClosedFormEngine: volatility must be positive");
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}
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const double disc = md.yield_curve().discount(T);
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const double sqrtT = std::sqrt(T);
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const double sig_sqrtT = sigma * sqrtT;
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if (sig_sqrtT < 1e-15) {
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const double forward = S * std::exp(r * T);
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switch (pk) {
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case PayoffKind::Call:
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return disc * std::max(0.0, forward - K);
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case PayoffKind::Put:
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return disc * std::max(0.0, K - forward);
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case PayoffKind::Digital:
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return (forward > K) ? disc : 0.0;
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}
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}
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const double d1 = (std::log(S / K) + (r + 0.5 * sigma * sigma) * T) / sig_sqrtT;
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const double d2 = d1 - sig_sqrtT;
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switch (pk) {
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case PayoffKind::Call:
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return S * norm_cdf(d1) - K * disc * norm_cdf(d2);
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case PayoffKind::Put:
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return K * disc * norm_cdf(-d2) - S * norm_cdf(-d1);
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case PayoffKind::Digital:
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return disc * norm_cdf(d2);
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}
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throw std::logic_error("BlackScholesClosedFormEngine: unhandled PayoffKind");
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}
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