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277 lines (277 loc) · 8.12 KB
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//#include "bs.h"
//#include <algorithm>
//#include <cmath>
//#include <boost/math/tools/toms748_solve.hpp>
//#include <mkl.h>
//#include "rando.h"
//
//
/////// Black-Scholes price : -1 put, 1 call
////double FBlsPrice(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig);
////
////
/////// Black-Scholes delta : -1 put, 1 call
////double BlsDelta(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig);
////
/////// Black-Scholes gamma : -1 put, 1 call
////double BlGamma(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig);
////
/////// Black-Scholes vega : -1 put, 1 call
////double BlsVega(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig);
////
/////// Black-Scholes implied voilatility: -1 put, 1 call
////double BlsImpliedVol(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double price);
////
////double NormCdf(double x);
//
//
//
//inline double BlsD1(double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// return (log(S / X) + (R - Q) * Trate + sig * sig * Tsigma / 2) / (sig * sqrt(Tsigma));
//}
//
//inline double BlsD2(double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// if (S == 0)
// {
// if (X == 0)
// return 20;
// else
// return -20;
// }
// if (X == 0) return 20;
//
// return (log(S / X) + (R - Q) * Trate - sig * sig * Tsigma / 2) / (sig * sqrt(Tsigma));
//}
//
//inline double BlsD2(double d1, double Tsigma, double sig)
//{
// return d1 - (sig * sqrt(Tsigma));
//}
//
//
//double BlsPrice2(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// double d1, d2;
// if (fabs(Tsigma) < 1e-8)
// {
// return std::max(CoP * (X - S), 0.);
// }
// d1 = BlsD1(S, X, R, Q, Trate, Tsigma, sig);
// d2 = BlsD2(d1, Tsigma, sig);
// double res = S * exp(-Q * Trate) * NormCdf(CoP * d1) - X * exp(-R * Trate) * NormCdf(CoP * d2);
// res *= CoP;
// // double put = - S * exp(-Q * Trate) * NormCdf(-d1) + X * exp(-R * Trate) * NormCdf(-d2);
// return res;
//}
//
//double BlsPrice(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// if (fabs(Tsigma) < 1e-8)
// return std::max(CoP * (X - S), 0.);
// double ssTs = sig * sqrt(Tsigma);
// double d1 = (log(S / X) + (R - Q) * Trate + sig * sig * Tsigma / 2) / (ssTs);
// double d2 = d1 - (ssTs);
// double res = S * exp(-Q * Trate) * NormCdf(CoP * d1) - X * exp(-R * Trate) * NormCdf(CoP * d2);
// res *= CoP;
// // double put = - S * exp(-Q * Trate) * NormCdf(-d1) + X * exp(-R * Trate) * NormCdf(-d2);
// return res;
//}
//
//double BlsPrice_noQ(double CoP, double S, double X, double R, double Trate, double Tsigma, double sig)
//{
// if (fabs(Tsigma) < 1e-8)
// return std::max(CoP * (X - S), 0.);
// double ssTs = sig * sqrt(Tsigma);
// double d1 = (log(S / X) + (R)*Trate + sig * sig * Tsigma / 2) / (ssTs);
// double d2 = d1 - (ssTs);
// double res = S * NormCdf(CoP * d1) - X * exp(-R * Trate) * NormCdf(CoP * d2);
// res *= CoP;
// // double put = - S * exp(-Q * Trate) * NormCdf(-d1) + X * exp(-R * Trate) * NormCdf(-d2);
// return res;
//}
//
//double BlsPrice_noQ2(double CoP, double S, double X, double R, double Trate, double Tsigma, double sig)
//{
// if (fabs(Tsigma) < 1e-8)
// return std::max(CoP * (X - S), 0.);
// double ssTs = sig * sqrt(Tsigma);
// double d1 = (log(S / X) + (R)*Trate + sig * sig * Tsigma / 2) / (ssTs);
// double d2 = d1 - (ssTs);
// double res = S * NormCdf(CoP * d1) - X * exp(-R * Trate) * NormCdf(CoP * d2);
// res *= CoP;
//
// double a = log(S / X);
// double b = -Trate * R;
// double sig_sig_two = sig * sig * 2.;
// double z = Tsigma * sig_sig_two;
//
// double c = 0.25 * z;
// double e = exp(b);
// double y = 1.0 / sqrt(z);
//
// double w1 = (a - b + c) * y;
// double w2 = (a - b - c) * y;
// d1 = erf(CoP * w1);
// d2 = erf(CoP * w2);
// d1 = 0.5 + 0.5 * d1;
// d2 = 0.5 + 0.5 * d2;
//
// res = S * d1 - X * e * d2;
// res *= CoP;
//
// return res;
//}
//
//
//
//double BlsDelta(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// double res;
// double d1 = BlsD1(S, X, R, Q, Trate, Tsigma, sig);
// res = CoP * exp(-Q * Trate) * NormCdf(CoP * d1);
// //put res = exp(-Q * T) * (rando::NormCdf(d1) - 1);
// return res;
//}
//
//double BlsGamma(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// double res;
// double unsursdt = 1 / (sig * sqrt(Tsigma));
// if (S < 1e-10) return 0;
// double d1 = BlsD1(S, X, R, Q, Trate, Tsigma, sig);
// res = exp(-Q * Trate) * NormPdf(d1) * unsursdt / S;
// return res;
//}
//
//double BlsVega(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double sig)
//{
// double res;
// double d1 = BlsD1(S, X, R, Q, Trate, Tsigma, sig);
// res = exp(-Q * Trate) * S * sqrt(Tsigma) * NormPdf(d1);
// return res;
//
//}
//
//
//double BlsImpliedVol(double CoP, double S, double X, double R, double Q, double Trate, double Tsigma, double price)
//{
// auto f = [=](double sig)
// {
// return BlsPrice(CoP, S, X, R, Q, Trate, Tsigma, S) - price;
// };
// std::uintmax_t max_iter{ 10 };
//
// auto pres =
// boost::math::tools::toms748_solve(
// f,
// 0.000001,
// 10.,
// boost::math::tools::eps_tolerance<double>{},
// max_iter);
// return pres.first;
//}
//
//
//double BlsImpliedVol_noQ(double CoP, double S, double X, double R, double Trate, double Tsigma, double price)
//{
// auto f = [=](double sig)
// {
// //fmt::print("{}/{}/{}")
// double pr = BlsPrice_noQ(CoP, S, X, R, Trate, Tsigma, sig);
// return pr - price;
// };
// std::uintmax_t max_iter{ 10 };
//
// auto pres =
// boost::math::tools::toms748_solve(
// f,
// 0.000001,
// 10.,
// boost::math::tools::eps_tolerance<double>{},
// max_iter);
// return pres.first;
//}
////
////inline double BlsD1(double F, double X, double Tsigma, double sig)
////{
//// return (log(F / X) + sig * sig * Tsigma / 2) / (sig * sqrt(Tsigma));
////}
//
//double FBlsPrice(double CoP, double F, double X, double DF, double Tsigma, double sig)
//{
// if (fabs(Tsigma) < 1e-8)
// return std::max(CoP * (X - F), 0.);
// double ssTs = sig * sqrt(Tsigma);
// double d1 = (log(F / X) + sig * sig * Tsigma / 2) / (ssTs);
// double d2 = d1 - (ssTs);
// double res = F * NormCdf(CoP * d1) - X * NormCdf(CoP * d2);
// res *= CoP * DF;
// return res;
//}
//
//double FBlsImpliedVol(double CoP, double F,double X, double df, double Tsigma, double price)
//{
// auto f = [=](double sig)
// {
// //fmt::print("{}/{}/{}")
// double pr = FBlsPrice(CoP, F, X, df, Tsigma, sig);
// return pr - price;
// };
// std::uintmax_t max_iter{ 10 };
//
// auto pres =
// boost::math::tools::toms748_solve(
// f,
// 0.000001,
// 10.,
// boost::math::tools::eps_tolerance<double>{},
// max_iter);
// return pres.first;
//
//}
//
//inline double FBlsD1(double F, double X, double Tsigma, double sig)
//{
// return (log(F / X) + sig * sig * Tsigma / 2) / (sig * sqrt(Tsigma));
//}
//
//inline
//double FBlsDelta(double CoP, double F, double X, double df, double Tsigma, double sig)
//{
// double res;
// double d1 = FBlsD1(F, X, Tsigma, sig);
// res = CoP * df * NormCdf(CoP * d1);
// return res;
//}
//
//inline
//double FBlsGamma(double /*CoP*/, double F, double X, double df, double Tsigma, double sig)
//{
// if (F < 1e-10) return 0;
// double res;
// double one_upon_sst = 1. / (sig * sqrt(Tsigma));
// double d1 = FBlsD1(F, X, Tsigma, sig);
// res = df * NormCdf(d1) * one_upon_sst / F;
// return res;
//}
//
//inline
//double FBlsVega(double /*CoP*/, double F, double X, double df, double Tsigma, double sig)
//{
// double res;
// double d1 = FBlsD1(F, X, Tsigma, sig);
// res = df * NormCdf(d1) * sqrt(Tsigma) * F;
// return res;
//
//}
//
//VolDeltaVega FInvBls(double CoP, double F, double X, double df, double Tsigma, double price)
//{
// VolDeltaVega res;
// res._implied_volatility = FBlsImpliedVol(CoP, F, X, df, Tsigma, price);
// res._delta = FBlsDelta(CoP, F, X, df, Tsigma, res._implied_volatility);
// res._vega= FBlsVega(CoP, F, X, df, Tsigma, res._implied_volatility);
// return res;
//}