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bs.c
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bs.c
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#include "mex.h"
#include <math.h>
/*
% BS Black-Scholes option pricing model
% USAGE
% V=bs(sigma,S,K,r,delta,T,put);
% INPUTS
% sigma : volatility
% S : price of underlying asset
% K : strike price
% r : interest rate on a discount bond
% delta : dividend rate
% T : time to expiration
% OUTPUT
% V : option premium
*/
double bs(double sigma,double S, double k, double r, double d, double T, bool put);
double cdfn(double x);
void mexFunction(
int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
{
mwSize n, nn, i; /*nn is mxGetNumberOfElements, n and i derive from nn.*/
double *V, *Vend, *temp; /*mxGetPr, V, mxGetPr*/
double *sigma, *S, *k, *r, *d, *T; /*mxGetPr,...,mxGetPr*/
int nsigma, nS,nk,nr,nd,nT,nput, nv, nd1; /*1 or 0*/
bool *putflag; /*true*/
/* Error checking on inputs */
if (nrhs<6) mexErrMsgTxt("Not enough input arguments.");
if (nrhs>7) mexErrMsgTxt("Too many input arguments.");
if (nlhs>2) mexErrMsgTxt("Too many output arguments.");
for (i=0; i<nrhs; i++)
{
if (!mxIsDouble(prhs[i]) && !mxIsSparse(prhs[i]))
mexErrMsgTxt("Function not defined for variables of input class");
if (mxIsComplex(prhs[i]))
mexErrMsgTxt("X must be real.");
}
sigma=mxGetPr(prhs[0]);
S=mxGetPr(prhs[1]);
k=mxGetPr(prhs[2]);
r=mxGetPr(prhs[3]);
d=mxGetPr(prhs[4]);
T=mxGetPr(prhs[5]);
n=1;
nn=mxGetNumberOfElements(prhs[0]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[0]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nsigma=1; else nsigma=0;
nn=mxGetNumberOfElements(prhs[1]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[1]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nS=1; else nS=0;
nn=mxGetNumberOfElements(prhs[2]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[2]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nk=1; else nk=0;
nn=mxGetNumberOfElements(prhs[3]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[3]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nr=1; else nr=0;
nn=mxGetNumberOfElements(prhs[4]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[4]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nd=1; else nd=0;
nn=mxGetNumberOfElements(prhs[5]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[5]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nT=1; else nT=0;
if (nrhs<7) {putflag=mxCalloc(1,sizeof(bool)); *putflag=false; nput=0;}
else
{
nn=mxGetNumberOfElements(prhs[6]);
if (n!=nn)
if (n==1) {n=nn; plhs[0]=mxDuplicateArray(prhs[6]);}
else if (nn>1) mexErrMsgTxt("Inputs are not size compatible");
if (nn>1) nput=1; else nput=0;
putflag=mxCalloc(nn,sizeof(bool));
temp=mxGetPr(prhs[6]);
for (i=0;i<nn;i++)
if (temp[i]==1) putflag[i]=true; else putflag[i]=false;
}
if (n==1) plhs[0]=mxCreateDoubleMatrix(1,1,mxREAL);
V=mxGetPr(plhs[0]);
Vend=V+n;
for (;V<Vend;V++)
{
*V=bs(*sigma,*S,*k,*r,*d,*T,*putflag);
sigma+=nsigma;
S+=nS;
k+=nk;
r+=nr;
d+=nd;
T+=nT;
putflag+=nput;
}
}
double bs(double sigma,double S, double k,double r,double d,double T,bool put)
{
double d1, sigmaT, SS, kk, V;
sigmaT=sigma*sqrt(T);
SS=exp(-d*T)*S;
kk=exp(-r*T)*k;
d1=log(SS/kk)/sigmaT + 0.5*sigmaT;
V=SS*cdfn(d1)-kk*cdfn(d1-sigmaT);
if (put) V=V-SS+kk;
return(V);
}
double cdfn(double x)
{
const double p1[5] = {
3.20937758913846947e03,
3.77485237685302021e02,
1.13864154151050156e02,
3.16112374387056560e00,
1.85777706184603153e-1};
const double q1[4] = {
2.84423683343917062e03,
1.28261652607737228e03,
2.44024637934444173e02,
2.36012909523441209e01};
const double p2[9] = {
1.23033935479799725e03,
2.05107837782607147e03,
1.71204761263407058e03,
8.81952221241769090e02,
2.98635138197400131e02,
6.61191906371416295e01,
8.88314979438837594e00,
5.64188496988670089e-1,
2.15311535474403846e-8};
const double q2[8] = {
1.23033935480374942e03,
3.43936767414372164e03,
4.36261909014324716e03,
3.29079923573345963e03,
1.62138957456669019e03,
5.37181101862009858e02,
1.17693950891312499e02,
1.57449261107098347e01};
const double p3[6] = {
6.58749161529837803e-4,
1.60837851487422766e-2,
1.25781726111229246e-1,
3.60344899949804439e-1,
3.05326634961232344e-1,
1.63153871373020978e-2};
const double q3[5] = {
2.33520497626869185e-3,
6.05183413124413191e-2,
5.27905102951428412e-1,
1.87295284992346047e00,
2.56852019228982242e00};
int i;
double xval, xx, p, q;
bool NegativeValue;
xval=x;
if (xval<0) {xval=-0.7071067811865475*xval; NegativeValue=true; }
else {xval= 0.7071067811865475*xval; NegativeValue=false;}
if (xval<=0.46875)
{
xx = xval*xval;
p=p1[4];
q=1.0;
for (i=3;i>=0;i--) {p=p*xx+p1[i]; q=q*xx+q1[i];}
xx=p/q;
xx *= xval;
if (NegativeValue) xx = 0.5*(1-xx); else xx = 0.5*(1+xx);
}
else if (xval<=4)
{
xx=xval;
p=p2[8];
q=1.0;
for (i=7;i>=0;i--) {p=p*xx+p2[i]; q=q*xx+q2[i];}
xx=p/q;
xx = exp(-xval*xval)*xx;
if (NegativeValue) xx=0.5*xx; else xx=1-0.5*xx;
}
else if (xval<10)
{
xx=1/(xval*xval);
p=p3[5];
q=1.0;
for (i=4;i>=0;i--) {p=p*xx+p3[i]; q=q*xx+q3[i];}
xx=p/q;
xx = exp(-xval*xval)*(0.7071067811865475-xx)/(xval);
if (mxIsNaN(xx)) xx=0.0;
if (NegativeValue) xx=0.5*xx; else xx=1-0.5*xx;
}
else
if (NegativeValue) xx=0; else xx=1;
return(xx);
}