double value(Option opt){
double s1=opt.spot*(CumulativeNormal(d(opt.spot/opt.Strike,opt.Expiry,opt,true))-CumulativeNormal(d(opt.spot/opt.Barrier,opt.Expiry,opt,true)));
double s2=-exp(-opt.Rate*opt.Expiry)* opt.Strike*(CumulativeNormal(d( opt.spot/ opt.Strike, opt.Expiry,opt,false)) - CumulativeNormal(d( opt.spot/ opt.Barrier,opt.Expiry,opt,false)));
double s3=-opt.Barrier*pow( opt.spot/ opt.Barrier,-2* opt.Rate/( opt.Vol* opt.Vol))*(CumulativeNormal(d( opt.Barrier* opt.Barrier/( opt.Strike* opt.spot), opt.Expiry,opt,true))-CumulativeNormal(d( opt.Barrier/ opt.spot, opt.Expiry,opt,true)));
double s4=exp(- opt.Rate* opt.Expiry)* opt.Strike*pow( opt.spot/ opt.Barrier,(-2* opt.Rate/( opt.Vol* opt.Vol)+1))*(CumulativeNormal(d( (opt.Barrier* opt.Barrier/( opt.Strike* opt.spot)),opt.Expiry,opt,false))-CumulativeNormal(d( (opt.Barrier/ opt.spot),opt.Expiry,opt,false)));
return s1+s2+s3+s4;
}
double CallOption::calc(double spot, double r, double d, double vol) {
double standardDeviation = vol*sqrt(t_);
double moneyness = log(spot / strike_);
double d1 = (moneyness + (r - d)*t_ + 0.5* standardDeviation*standardDeviation) / standardDeviation;
double d2 = d1 - standardDeviation;
double price = spot*exp(-d*t_) * CumulativeNormal(d1)
- strike_*exp(-r*t_)*CumulativeNormal(d2);
return price;
}
double CallBS(const Wrapper<Parameter>& r, const Wrapper<Parameter>& sig, double Expiry,double Spot, double Strike)
{
double d1,d2;
d1=1./(sig->Mean(1,2)*sqrt(Expiry)) * ( log(Spot/Strike) + (r->Mean(1,2) + .5 * sig->Mean(1,2) * sig->Mean(1,2) ) * Expiry);
d2=1./(sig->Mean(1,2)*sqrt(Expiry)) * ( log(Spot/Strike) + (r->Mean(1,2) - .5 * sig->Mean(1,2) * sig->Mean(1,2) ) * Expiry);
double ans = CumulativeNormal(d1) * Spot - CumulativeNormal(d2) * Strike * exp(-r->Mean(1,2) * Expiry);
return ans;
}
VAttrList
VBayes(VImage cbeta_images[], VImage sd_images[], int nimages, VBoolean level, VBoolean zscore) {
VAttrList out_list = NULL;
VImage dest = NULL, sigma_image = NULL;
int i, j, k, npixels;
VFloat *dest_pp, *beta_pp[N], *sd_pp[N], *sigma_pp = NULL;
VFloat pmin, pmax;
double mean = 0, sigma = 0;
float rx, wsum, msum, w0, wx, s, msumold;
float result = 0;
float gmean[N], gvar[N];
float tiny = 1.0e-12;
/*
** create output image
*/
dest = VCopyImage(cbeta_images[0], NULL, VAllBands);
if(!dest)
return NULL;
VFillImage(dest, VAllBands, 0);
VSetAttr(VImageAttrList(dest), "num_images", NULL, VShortRepn, (VShort)nimages);
VSetAttr(VImageAttrList(dest), "modality", NULL, VStringRepn, "bayes_map");
VSetAttr(VImageAttrList(dest), "name", NULL, VStringRepn, "bayes");
if(level == TRUE) {
VSetAttr(VImageAttrList(dest), "modality", NULL, VStringRepn, "mean");
VSetAttr(VImageAttrList(dest), "name", NULL, VStringRepn, "mean");
sigma_image = VCopyImage(dest, NULL, VAllBands);
if(!sigma_image)
return NULL;
VFillImage(sigma_image, VAllBands, 0);
VSetAttr(VImageAttrList(sigma_image), "num_images", NULL, VShortRepn, (VShort)nimages);
VSetAttr(VImageAttrList(sigma_image), "modality", NULL, VStringRepn, "std_dev");
VSetAttr(VImageAttrList(sigma_image), "name", NULL, VStringRepn, "std_dev");
}
/*
** for each voxel
*/
pmax = VRepnMinValue(VFloatRepn);
pmin = VRepnMaxValue(VFloatRepn);
npixels = VImageNPixels(cbeta_images[0]);
for(i = 0; i < nimages; i++) {
beta_pp[i] = (VFloat *) VImageData(cbeta_images[i]);
sd_pp[i] = (VFloat *) VImageData(sd_images[i]);
}
dest_pp = (VFloat *) VImageData(dest);
if(level == TRUE)
sigma_pp = (VFloat *) VImageData(sigma_image);
for(j = 0; j < npixels; j++) {
if(j % 10000 == 0)
fprintf(stderr, "...%.2f%%\r", (float)100 * j / (float)npixels);
result = mean = sigma = 0;
/*
** read data from input images
*/
for(k = 0; k < nimages; k++) {
gmean[k] = *beta_pp[k]++; /* mean c*beta */
rx = *sd_pp[k]++; /* standard deviation of c*beta*/
gvar[k] = rx * rx; /* variation of c*beta*/
}
/* see Box,Tiao, pp.17-18 calculate probability distribution */
wsum = 0;
msum = 0;
w0 = 0;
for(k = 0; k < nimages; k++) { /* for each image */
s = gvar[k];
if(s < tiny)
goto next;
s = sqrt((double)s);
if(s < tiny)
goto next;
wx = 1.0 / (s * s);
wsum = w0 + wx;
msumold = msum;
msum = (w0 * msum + wx * gmean[k]) / wsum;
w0 = wsum;
sigma = 1.0 / sqrt(wsum);
}
if(wsum < tiny)
goto next;
/* resulting mean and std dev */
mean = msum;
sigma = 1.0 / sqrt(wsum);
if(level == TRUE) {
result = mean;
goto next;
}
/* calculate probability under distribution */
result = CumulativeNormal(mean, sigma);
/* output */
if(zscore) {
/* CHECK HERE IF "1.0-" is correct */
result = (float)p2z((double)(1.0 - result));
if(mean < 0)
result = -result;
if(result > 20)
result = 20;
if(result < -20)
result = -20;
} else {
result *= 100.0;
if(result > 100)
result = 100;
if(mean < 0)
result = -result;
}
if(result < pmin)
pmin = result;
if(result > pmax)
pmax = result;
next:
*dest_pp++ = result;
if(level)
*sigma_pp++ = sigma;
}
out_list = VCreateAttrList();
fprintf(stderr, "...100.00%%\n");
if(level == FALSE) {
fprintf(stderr, "\n min: %.3f, max: %.3f\n", pmin, pmax);
VAppendAttr(out_list, "zmap", NULL, VImageRepn, dest);
return out_list;
} else {
VAppendAttr(out_list, "mean", NULL, VImageRepn, dest);
VAppendAttr(out_list, "std_dev", NULL, VImageRepn, sigma_image);
return out_list;
}
return NULL;
}