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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: liborser.cpp
Revision: $Id$
Contents: example for differentiation of OpemMP parallel programs
serial version for comparisons
Copyright (c) Andrea Walther
This file is part of ADOL-C. This software is provided as open source.
Any use, reproduction, or distribution of the software constitutes
recipient's acceptance of the terms of the accompanying license file.
---------------------------------------------------------------------------*/
/* Program to compute deltas and vegas of swaption portfolio
from forward and reverse mode pathwise sensitivities
in parallel written by Andrea Walther in 2008-11 based on
code written by written by Mike Giles in 2005-7 which is
again based on code written by Zhao and Glasserman at
Columbia University */
using namespace std;
#include <stdlib.h>
#include <stdio.h>
#include <ctime>
#include <cmath>
#include <adolc/adolc.h>
/* calculate path values */
template <typename ADdouble>
void path_calc(const int N, const int Nmat, const double delta,
ADdouble L[], const double lambda[], ADdouble z[])
{
int i, n;
double lam, con1;
ADdouble v, vrat;
ADdouble sqez;
for(n=0; n<Nmat; n++) {
sqez = sqrt(delta)*z[n];
v = 0.0;
for (i=n+1; i<N; i++) {
lam = lambda[i-n-1];
con1 = delta*lam;
v += (con1*L[i])/(1.0+delta*L[i]);
vrat = exp(con1*v + lam*(sqez-0.5*con1));
L[i] = L[i]*vrat;
}
}
}
/* calculate the portfolio value v */
template <typename ADdouble>
void portfolio(const int N, const int Nmat, const double delta,
const int Nopt, const int maturities[],
const double swaprates[],
const ADdouble L[], ADdouble& v )
{
int i, m, n;
ADdouble b, s, swapval, *B, *S;
B = new ADdouble[N];
S = new ADdouble[N];
b = 1.0;
s = 0.0;
for (n=Nmat; n<N; n++) {
b = b/(1.0+delta*L[n]);
s = s + delta*b;
B[n] = b;
S[n] = s;
}
v = 0;
for (i=0; i<Nopt; i++){
m = maturities[i] + Nmat-1;
swapval = B[m] + swaprates[i]*S[m] - 1.0;
condassign(v,-swapval,v-100.0*swapval);
}
// apply discount //
for (n=0; n<Nmat; n++)
v = v/(1.0+delta*L[n]);
delete[](B);
delete[](S);
}
/* -------------------------------------------------------- */
int main(){
// LIBOR interval //
double delta = 0.25;
// data for swaption portfolio //
int Nopt = 15;
int maturities[] = {4,4,4,8,8,8,20,20,20,28,28,28,40,40,40};
double swaprates[] = {.045,.05,.055,.045,.05,.055,.045,.05,
.055,.045,.05,.055,.045,.05,.055 };
int i, j, N, Nmat, npath;
double vtot, *v, *lambda, **z,**grad, *gradtot, **xp;
Nmat = 40;
N = Nmat+40;
npath = 30;
lambda = new double[N];
v = new double[npath];
gradtot = new double[N];
z = new double*[npath];
grad = new double*[npath];
xp = new double*[npath];
for (i=0;i<npath;i++)
{
z[i] = new double[Nmat];
grad[i] = new double[N+Nmat];
xp[i] = new double[N+Nmat];
}
for (i=0;i<N;i++)
{
gradtot[i] = 0.0;
lambda[i] = 0.2;
}
for (j=0; j<npath; j++)
{
v[j] = 0;
for (i=0; i<N; i++)
xp[j][i]= 0.05;
for (i=0; i<Nmat; i++)
{
z[j][i] = 0.3;
xp[j][N+i]= 0.3;
}
}
//----------------------------------------------------------//
// //
// do a full path + portfolio sensitivity check //
// //
// A real application would generate a different random //
// vector z for each path but here we set one and reuse it //
// //
//----------------------------------------------------------//
adouble *La, va, *za;
La = new adouble[N];
za = new adouble[Nmat];
trace_on(1);
for(j=0;j<N;j++)
La[j] <<= 0.050000;
for(j=0;j<Nmat;j++)
za[j] <<= z[0][j];
path_calc(N,Nmat,delta,La,lambda,za);
portfolio(N,Nmat,delta,Nopt,maturities,swaprates,La,va);
va >>= v[i];
trace_off(1);
for(i=0;i<npath;i++)
gradient(1,N+Nmat,xp[i],grad[i]);
delete[] (La);
vtot = 0;
for (i=0; i<npath; i++)
{
vtot += v[i];
for(j=0;j<N;j++)
gradtot[j] += grad[i][j];
}
vtot = vtot/npath;
for(j=0;j<N;j++)
gradtot[j] /= npath;
printf("Gradient: \n");
for(i=0;i<N;i++)
printf(" %f \n",gradtot[i]);
return 0;
}
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