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asian.h
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asian.h
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//
// Dale Roberts <dale.o.roberts@gmail.com>
//
#ifndef volmodels_asian_h
#define volmodels_asian_h
#include <stdio.h>
#include <vector>
#include <algorithm>
#include <boost/random.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include "exact.h"
#include "sobolpoints.h"
#include "scramblepoints.h"
#include "sobol.h"
#include "utils.h"
#include "bridges.h"
#include "stats.h"
#include "matlab.h"
using namespace std;
Result MCAsian(double r, double rho, double kappa, double theta, double sigma, double v0, double S0, const vector<double>& times, double K, long numberPaths, long numberBatches, long prsSeed)
{
vector<double> outerStats;
int tsteps = times.size();
int tdim = tsteps-1;
double tmax = *times.rbegin();
#pragma omp parallel shared(outerStats)
{
#pragma omp for
for (long k=0; k < numberBatches; k++)
{
vector<double> innerStats;
// new random number generator for each batch
boost::mt19937 rng(prsSeed + k * numberPaths);
boost::uniform_real<> uni_dist(0,1);
boost::variate_generator<boost::mt19937&, boost::uniform_real<> > uni(rng, uni_dist);
for (unsigned long i=0; i < numberPaths; i++)
{
vector<double> Ss(tsteps, S0);
vector<double> Vs(tsteps, v0);
double p;
for(long j = 1; j < tsteps; j++)
{
p = uni();
Ss[j] = quantileHestonProcess(p, uni(), uni(), r, rho, kappa, theta, sigma, times[j-1], Vs[j-1], Ss[j-1], times[j]);
Vs[j] = quantileSquareRootProcess(p, kappa, theta, sigma, times[j-1], Vs[j-1], times[j]);
}
double meanprice = 0.0;
for (std::vector<double>::iterator jj = Ss.begin() + 1; jj != Ss.end(); ++jj) {
meanprice += *jj;
}
meanprice = meanprice / tdim;
double payoff = meanprice - K;
payoff = (payoff>0? payoff : 0) * exp(-r*tmax);
innerStats.push_back(payoff);
}
double mean = Mean(innerStats);
#pragma omp critical
outerStats.push_back(mean);
}
}
double mean = Mean(outerStats);
double stderr = StdError(outerStats);
return Result(mean, stderr);
}
Result QMCAsian(double r, double rho, double kappa, double theta, double sigma, double v0, double S0, const vector<double>& times, double K, long numberPaths, long numberBatches, long prsSeed)
{
using boost::numeric::ublas::matrix;
vector<double> outerStats;
int tsteps = times.size();
int tdim = tsteps - 1;
int sact = 3*tdim+1;
double tmax = *times.rbegin();
srand(prsSeed);
int m = 16, s = 1000;
matrix<bool> mat(m*s, m);
getSobolpoints(mat);
int Kscramble=31;
if(!isPowerOfTwo(numberPaths)) {
cout << "numberPaths not a power of two!" << endl;
return Result(0., 0.);
}
int mact = log2(numberPaths);
#pragma omp parallel shared(outerStats, mat)
{
#pragma omp for
for (long k=0; k < numberBatches; k++)
{
vector<double> innerStats;
// P will contain the scrambled points
matrix<double> P(sact, numberPaths);
#pragma omp critical
getscrambledpoints(P, mat, sact, mact, m, Kscramble, numberPaths);
for (long i=0; i < numberPaths; i++)
{
vector<double> Ss(tsteps, S0);
vector<double> Vs(tsteps, v0);
for(long j = 1; j < tsteps; j++)
{
Ss[j] = quantileHestonProcess(P(3*(j-1),i), P(3*(j-1)+1,i), P(3*(j-1)+2,i), r, rho, kappa, theta, sigma, times[j-1], Vs[j-1], Ss[j-1], times[j]);
Vs[j] = quantileSquareRootProcess(P(3*(j-1),i), kappa, theta, sigma, times[j-1], Vs[j-1], times[j]);
}
double meanprice = 0.0;
for (std::vector<double>::iterator jj = Ss.begin() + 1; jj != Ss.end(); ++jj) {
meanprice += *jj;
}
meanprice = meanprice / tdim;
double payoff = meanprice - K;
payoff = (payoff>0? payoff : 0) * exp(-r*tmax);
innerStats.push_back(payoff);
}
double mean = Mean(innerStats);
#pragma omp critical
outerStats.push_back(mean);
}
}
double mean = Mean(outerStats);
double stderr = StdError(outerStats);
return Result(mean, stderr);
}
Result QMCAsianBridge(double r, double rho, double kappa, double theta, double sigma, double v0, double S0, const vector<double>& times, double K, long numberPaths, long numberBatches, long prsSeed)
{
using boost::numeric::ublas::matrix;
using boost::numeric::ublas::matrix_column;
vector<double> outerStats;
int tsteps = times.size();
int tdim = tsteps - 1;
int sact = 3*(tdim-1)+2*tdim+1;
double tmax = *times.rbegin();
srand(prsSeed);
int m = 16, s = 1000;
matrix<bool> mat(m*s, m);
getSobolpoints(mat);
int Kscramble=31;
if(!isPowerOfTwo(numberPaths)) {
cout << "numberPaths not a power of two!" << endl;
return Result(0., 0.);
}
int mact = log2(numberPaths);
#pragma omp parallel shared(outerStats, mat)
{
#pragma omp for
for (int k=0; k < numberBatches; k++)
{
vector<double> innerStats;
// P will contain the scrambled points
matrix<double> P(sact, numberPaths);
#pragma omp critical
getscrambledpoints(P, mat, sact, mact, m, Kscramble, numberPaths);
#ifdef DEBUG
ostringstream filename;
filename << "rep" << k+1 << ".dlm";
ReadMatlabMatrix(filename.str(), P);
P = boost::numeric::ublas::trans(P);
matrix<double> result;
ReadMatlabMatrix("result.dlm", result);
result = boost::numeric::ublas::trans(result);
#endif
for (long i=0; i < numberPaths; i++)
{
// extract a column from the scrambled points
matrix_column<matrix<double>> Pc(P,i);
// generate the value of the square root process at the time points
std::vector<double> qs(Pc.begin(), Pc.begin()+3*(tdim-1)+1);
std::vector<double> Vs = squareRootBridge(times, kappa, theta, sigma, v0, qs);
// generate the integrals of V and the stochastic integrals of sqrt(V)
qs.assign(Pc.begin()+3*(tdim-1)+1, Pc.begin()+3*(tdim-1)+tsteps+1);
std::vector<double> intVs(tsteps, 0.0);
std::vector<double> intsqrVdWs(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
intVs[j] = quantileIntSquareRootProcess(qs[j-1], kappa, theta, sigma, times[j-1], Vs[j-1], times[j], Vs[j]);
intsqrVdWs[j] = (Vs[j] - Vs[j-1] - kappa*theta*(times[j]-times[j-1]) + kappa * intVs[j]) / sigma;
}
// PIO(qs);
// PIO(times);
// PIO(Vs);
// PIO(intVs);
// PIO(intsqrVdWs);
// generate the corrected drifts and vols
std::vector<double> drifts(tsteps, log(S0));
std::vector<double> vols(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
drifts[j] = drifts[j-1] + r*(times[j]-times[j-1]) - 0.5*intVs[j] + rho*intsqrVdWs[j];
vols[j] = vols[j-1] + (1-rho*rho)*intVs[j];
}
qs.assign(Pc.begin()+3*(tdim-1)+tsteps, Pc.end());
std::vector<double> Ss = stockPriceBridge(times, drifts, vols, qs);
// PIO(times);
// PIO(drifts);
// PIO(vols);
// PIO(Ss);
double meanprice = 0.0;
for (std::vector<double>::iterator jj = Ss.begin() + 1; jj != Ss.end(); ++jj) {
meanprice += *jj;
}
meanprice = meanprice / tdim;
double payoff = meanprice - K;
payoff = (payoff>0? payoff : 0) * exp(-r*tmax);
innerStats.push_back(payoff);
// PO(payoff);
}
double mean = Mean(innerStats);
#ifdef DEBUG
printf("%.6f || %.6f\n", result(0,k), mean);
#endif
#pragma omp critical
outerStats.push_back(mean);
}
}
double mean = Mean(outerStats);
double stderr = StdError(outerStats);
return Result(mean, stderr);
}
Result QMCAsianBridge2(double r, double rho, double kappa, double theta, double sigma, double v0, double S0, const vector<double>& times, double K, long numberPaths, long numberBatches, long prsSeed)
{
using boost::numeric::ublas::matrix;
using boost::numeric::ublas::matrix_row;
using boost::numeric::ublas::column_major;
vector<double> outerStats;
int tsteps = times.size();
int tdim = tsteps - 1;
int sact = 3*(tdim-1)+2*tdim+1;
double tmax = *times.rbegin();
#pragma omp parallel shared(outerStats)
{
#pragma omp for
for (int k=0; k < numberBatches; k++)
{
vector<double> innerStats;
// P will contain the scrambled points
matrix<double, column_major> P(numberPaths, sact);
#pragma omp critical
ScrambleSobol(prsSeed + k*numberBatches, P);
for (long i=0; i < numberPaths; i++)
{
// extract a row from the scrambled points
matrix_row<matrix<double, column_major>> Pc(P,i);
// generate the value of the square root process at the time points
std::vector<double> qs(Pc.begin(), Pc.begin()+3*(tdim-1)+1);
std::vector<double> Vs = squareRootBridge(times, kappa, theta, sigma, v0, qs);
// generate the integrals of V and the stochastic integrals of sqrt(V)
qs.assign(Pc.begin()+3*(tdim-1)+1, Pc.begin()+3*(tdim-1)+tsteps+1);
std::vector<double> intVs(tsteps, 0.0);
std::vector<double> intsqrVdWs(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
intVs[j] = quantileIntSquareRootProcess(qs[j-1], kappa, theta, sigma, times[j-1], Vs[j-1], times[j], Vs[j]);
intsqrVdWs[j] = (Vs[j] - Vs[j-1] - kappa*theta*(times[j]-times[j-1]) + kappa * intVs[j]) / sigma;
}
// generate the corrected drifts and vols
std::vector<double> drifts(tsteps, log(S0));
std::vector<double> vols(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
drifts[j] = drifts[j-1] + r*(times[j]-times[j-1]) - 0.5*intVs[j] + rho*intsqrVdWs[j];
vols[j] = vols[j-1] + (1-rho*rho)*intVs[j];
}
qs.assign(Pc.begin()+3*(tdim-1)+tsteps, Pc.end());
std::vector<double> Ss = stockPriceBridge(times, drifts, vols, qs);
double meanprice = 0.0;
for (std::vector<double>::iterator jj = Ss.begin() + 1; jj != Ss.end(); ++jj) {
meanprice += *jj;
}
meanprice = meanprice / tdim;
double payoff = meanprice - K;
payoff = (payoff>0? payoff : 0) * exp(-r*tmax);
innerStats.push_back(payoff);
}
double mean = Mean(innerStats);
#pragma omp critical
outerStats.push_back(mean);
}
}
double mean = Mean(outerStats);
double stderr = StdError(outerStats);
return Result(mean, stderr);
}
Result QMCEurosBridge(double r, double rho, double kappa, double theta, double sigma, double v0, double S0, const vector<double>& times, double K, long numberPaths, long numberBatches, long prsSeed)
{
using boost::numeric::ublas::matrix;
using boost::numeric::ublas::matrix_row;
using boost::numeric::ublas::column_major;
int tsteps = times.size();
int tdim = tsteps - 1;
int sact = 3*(tdim-1)+2*tdim+1;
vector<double> outerStats1;
vector<double> outerStats2;
vector<double> outerStats3;
vector<double> outerStats4;
vector<double> debugStats1;
#pragma omp parallel shared(outerStats1,outerStats2,outerStats3,outerStats4)
{
#pragma omp for
for (int k=0; k < numberBatches; k++)
{
vector<double> innerStats1;
vector<double> innerStats2;
vector<double> innerStats3;
vector<double> innerStats4;
// P will contain the scrambled points
matrix<double, column_major> P(numberPaths, sact);
#pragma omp critical
ScrambleSobol(prsSeed + k*numberBatches, P);
for (long i=0; i < numberPaths; i++)
{
// extract a row from the scrambled points
matrix_row<matrix<double, column_major>> Pc(P,i);
// vector<double> Pc = {0.9495, 0.4886, 0.1993, 0.4592, 0.9332, 0.8714, 0.7465, 0.5993, 0.9445, 0.9948, 0.9969, 0.3889, 0.0325, 0.0521, 0.2327, 0.3398, 0.4730, 0.5293 };
// generate the value of the square root process at the time points
std::vector<double> qs(Pc.begin(), Pc.begin()+3*(tdim-1)+1);
// PIO(qs);
std::vector<double> Vs = squareRootBridge(times, kappa, theta, sigma, v0, qs);
// PIO(Vs);
// generate the integrals of V and the stochastic integrals of sqrt(V)
qs.assign(Pc.begin()+3*(tdim-1)+1, Pc.begin()+3*(tdim-1)+tsteps+1);
// PIO(qs);
std::vector<double> intVs(tsteps, 0.0);
std::vector<double> intsqrVdWs(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
intVs[j] = quantileIntSquareRootProcess(qs[j-1], kappa, theta, sigma, times[j-1], Vs[j-1], times[j], Vs[j]);
intsqrVdWs[j] = (Vs[j] - Vs[j-1] - kappa*theta*(times[j]-times[j-1]) + kappa * intVs[j]) / sigma;
}
// PIO(intVs);
// PIO(intsqrVdWs);
// generate the corrected drifts and vols
std::vector<double> drifts(tsteps, log(S0));
std::vector<double> vols(tsteps, 0.0);
for (int j=1; j < tsteps; ++j) {
drifts[j] = drifts[j-1] + r*(times[j]-times[j-1]) - 0.5*intVs[j] + rho*intsqrVdWs[j];
vols[j] = vols[j-1] + (1-rho*rho)*intVs[j];
}
qs.assign(Pc.begin()+3*(tdim-1)+tsteps, Pc.end());
// PIO(qs);
std::vector<double> Ss = stockPriceBridge(times, drifts, vols, qs);
// PIO(Ss);
// double payoff1 = Ss[1];
double payoff1 = Ss[1] - K;
double payoff2 = Ss[2] - K;
double payoff3 = Ss[3] - K;
double payoff4 = Ss[4] - K;
payoff1 = (payoff1>0? payoff1 : 0) * exp(-r*times[1]);
payoff2 = (payoff2>0? payoff2 : 0) * exp(-r*times[2]);
payoff3 = (payoff3>0? payoff3 : 0) * exp(-r*times[3]);
payoff4 = (payoff4>0? payoff4 : 0) * exp(-r*times[4]);
innerStats1.push_back(payoff1);
innerStats2.push_back(payoff2);
innerStats3.push_back(payoff3);
innerStats4.push_back(payoff4);
// if (payoff1 < 1) {
// printf("%6.4f : ", payoff1);
// for(int i = 0; i < Pc.size(); ++i) {
// printf("%6.4f ", Pc[i]);
// }
// printf("\n");
// }
double debug1 = *max_element(intVs.begin(), intVs.end());
#pragma omp critical
debugStats1.push_back(debug1);
}
double mean1 = Mean(innerStats1);
double mean2 = Mean(innerStats2);
double mean3 = Mean(innerStats3);
double mean4 = Mean(innerStats4);
#pragma omp critical
{
outerStats1.push_back(mean1);
outerStats2.push_back(mean2);
outerStats3.push_back(mean3);
outerStats4.push_back(mean4);
}
}
}
PIO(debugStats1);
printf("%6i & ", numberPaths);
printf("%6.4f (%6.4f) & ", Mean(outerStats1), StdError(outerStats1));
printf("%6.4f (%6.4f) & ", Mean(outerStats2), StdError(outerStats2));
printf("%6.4f (%6.4f) & ", Mean(outerStats3), StdError(outerStats3));
printf("%6.4f (%6.4f) \\\\\n", Mean(outerStats4), StdError(outerStats4));
}
#endif