void main()
{
double thetas[] = {1,1,1,1,1};
double x[] = {0.82,1.1,1.42,1.58,2.0,2.19,2.3,2.5,2.7};
double y[] = {8.3,13.5,20.0,23.5,35.0,40.0,43.0,46.0,50.0};
int size = sizeof(thetas)/sizeof(double);
int sizex = sizeof(x)/sizeof(double);
int i= 0;
printf("%f\n",Htheta(thetas,1,size));
printf("%f\n",toerr(thetas,x,y,size,sizex));
fitto(thetas,x,y,size,sizex);
printf("%f\n",toerr(thetas,x,y,size,sizex));
printf("%f %f %f %f %f \n",thetas[0],thetas[1],thetas[2],thetas[3],thetas[4]);
for(i=0;i<sizex;i++)
{
printf("%f %f\n",x[i],Htheta(thetas,x[i],size));
}
}
double toerr(double *thetas,double *x, double *y,int sizeth,int sizex)
{
double total = 0;
int counter = 0;
int i = 0;
for(i=0;i<sizex;i++)
{
total = total + y[i] - Htheta(thetas,x[i],sizeth);
}
return total;
}
double toerr(double *thetas,double *x, double *y,int sizeth,int sizex) //find total error for given coeffs
{
double total = 0;
int counter = 0;
int i = 0;
for(i=0;i<sizex;i++)
{
total = total + y[i] - Htheta(thetas,x[i],sizeth);
}
return total;
}
void fitto(double *thetas,double *x, double *y,int sizeth,int sizex)
{
double newth[sizeth]; //temporary thetas
double rate = 1 * pow(10,(sizeth * -1)); //learning rate
double error = 100;
int i =0;
int j = 0;
int counter = 0;
for(i=0;i<sizeth;i++) //clear temp thetas
{
newth[i] = 0.0;
}
while(fabs(error) > 0.01)
{
for(j=0;j<sizeth;j++)
{
//printf("%d ",j);
for(i=0;i<sizex;i++)
{
newth[j] += rate * ((y[i] - Htheta(thetas,x[i],sizeth)) * pow(x[i],(double)j));
// printf("%f ",newth[j]);
}
//printf("\n");
}
for(j=0;j<sizeth;j++)
{
thetas[j] = thetas[j] + newth[j];
newth[j] = 0;
}
//printf("%f %f %f %f %f\n",thetas[0],thetas[1],thetas[2],thetas[3],thetas[4]);
if(counter % 10000 == 0)
printf("%f\n",toerr(thetas,x,y,sizeth,sizex));
counter++;
error = toerr(thetas,x,y,sizeth,sizex);
}
printf("%f\n",rate);
}
double fitto(double *thetas,double *x, double *y,int sizeth,int sizex,double lrate) //perform fitting of polynomial to data
{
double newth[sizeth]; //temporary thetas
double rate = lrate * pow(10,(sizeth * -1)); //learning rate
double error = 100;
int i =0;
int j = 0;
int counter = 0;
for(i=0;i<sizeth;i++) //clear temp thetas
{
newth[i] = 0.0;
}
while((fabs(error) > 0.01) && (counter < 1000000)) //carry on unitl error is less than 0.01 or 1 million interations have been carried out
{
for(j=0;j<sizeth;j++) //for each coeff
{
for(i=0;i<sizex;i++) //for each data point
{
newth[j] += rate * ((y[i] - Htheta(thetas,x[i],sizeth)) * pow(x[i],(double)j)); //find update value
}
}
for(j=0;j<sizeth;j++) //update coeffs
{
thetas[j] = thetas[j] + newth[j];
newth[j] = 0;
}
counter++;
error = toerr(thetas,x,y,sizeth,sizex);
}
return error;
}
double PathDepOption::PriceByMC(BSModel Model, long N, double epsilon)
{
double H=0.0; double Hsq=0.0;
int d = Model.S0.size();
SamplePath S(m);
Matrix C = Model.C;
Matrix CZ(d);
for(int i=0;i<d;i++) CZ[i].resize(m);
delta.resize(d); rho.resize(d); vega.resize(d); theta.resize(d); gamma.resize(d);
Vector Hdelta(d), Hvega(d), Hrho(d), Htheta(d), Hgamma(d);
for (int i=0; i<d; i++)
{
delta[i] = 0.0; Hdelta[i] = 0.0; Hvega[i] = 0.0; Hrho[i] = 0.0; Htheta[i] = 0.0;
}
for(long i=0; i<N; i++)
{
Model.GenerateSamplePath(T,m,S);
GetZ(CZ, S, C, Model.S0, Model.r, T/m);
H = (i*H + Payoff(S))/(i+1.0);
Hsq = (i*Hsq + pow(Payoff(S),2.0))/(i+1.0);
for (int j=0; j<d; j++)
{
Vector S0tmp = Model.S0;
S0tmp[j] = (1.0+epsilon)*S0tmp[j];
Matrix Cvega = C;
Cvega[j] = (1.0 + epsilon)*C[j];
Rescale(S, CZ, C, S0tmp, Model.r, T/m);
Hdelta[j] = (i*Hdelta[j] + Payoff(S)) / (i+1.0);
Rescale(S, CZ, C, Model.S0, Model.r*(1.0+epsilon), T/m);
Hrho[j] = (i*Hrho[j] + Payoff(S)) / (i+1.0);
Rescale(S, CZ, Cvega, Model.S0, Model.r, T/m);
Hvega[j] = (i*Hvega[j] + Payoff(S)) / (i+1.0);
Rescale(S, CZ, C, Model.S0, Model.r, T*(1.0+epsilon)/m);
Htheta[j] = (i*Htheta[j] + Payoff(S)) / (i+1.0);
S0tmp[j] = (1.0-epsilon)*Model.S0[j];
Rescale(S, CZ, C, S0tmp, Model.r, T/m);
Hgamma[j] = (i*Hgamma[j] + Payoff(S)) / (i+1.0);
Rescale(S, CZ, C, Model.S0, Model.r, T/m);
}
}
for(int i=0; i<d; i++)
{
delta[i] = exp(-Model.r*T) * ( Hdelta[i] - H ) / (epsilon*Model.S0[i]);
rho[i] = (exp(-Model.r*T*(1.0+epsilon))*Hrho[i] - exp(-Model.r*T)*H)/(epsilon*Model.r);
vega[i] = exp(-Model.r*T) * (Hvega[i] - H) / (epsilon*sqrt(C[i]^C[i]));
theta[i] = -1.0*(exp(-Model.r*T*(1.0+epsilon))*Htheta[i] - exp(-Model.r*T)*H)/(epsilon*T);
gamma[i] = exp(-Model.r*T)*(Hdelta[i]-2.0*H+Hgamma[i])/(Model.S0[i]*Model.S0[i]*epsilon*epsilon);
}
Price = exp(-Model.r*T)*H;
PricingError = exp(-Model.r*T)*sqrt(Hsq-H*H)/sqrt(N-1.0);
return Price;
}
