// Pricing a Lookback European Put option
double lookback_put(const double& S,
const double& M, // Maximum price of asset over period
const double& r,
const double& v,
const double& T) {
double a1 = a_1(S,M,r,v,T);
double a2 = a_2(S,M,r,v,T);
double a3 = a_3(S,M,r,v,T);
double term1 = -S * norm_cdf(-a1);
double term2 = M * exp(-r*T) * norm_cdf(-a2);
double mult = S*v*v/(2.0*r);
double term3 = norm_cdf(a1) - exp(-r*T) * pow((M/S),((2*r)/(v*v))) * norm_cdf(a3);
return term1 + term2 + mult * term3;
}
// Pricing a Lookback European Call option
double lookback_call(const double& S,
const double& m, // Minimum price of asset over period
const double& r,
const double& v,
const double& T) {
double a1 = a_1(S,m,r,v,T);
double a2 = a_2(S,m,r,v,T);
double a3 = a_3(S,m,r,v,T);
double term1 = S * norm_cdf(a1);
double term2 = m * exp(-r*T) * norm_cdf(a2);
double mult = S*v*v/(2.0*r);
double term3 = norm_cdf(-a1) - exp(-r*T) * pow((m/S),((2*r)/(v*v))) * norm_cdf(-a3);
return term1 - term2 - mult * term3;
}
void roll2(double a[], long ioff, long istd, long n, long n2, double ws[])
{
#undef ws_1
#define ws_1(a1) ws[a1-1]
#undef a_3
#define a_3(a1,a2,a3) a[a1-1+istd*(a2-1+n*(a3-1))]
/*c
c a double precision a_3(istd,n,n2)
c to be "rolled", in place, on its middle dimension
c
c ioff the offset by which to "roll" a_3 (iabs(ioff) .lt. n)
c for ioff>0:
c output a_3(1+ioff)= input a_3(1)
c output a_3(2+ioff)= input a_3(2)
c ... ...
c output a_3(n-1)= input a_3(n-ioff-1)
c output a_3(n)= input a_3(n-ioff)
c output a_3(1)= input a_3(n-ioff+1)
c output a_3(2)= input a_3(n-ioff+2)
c ... ...
c output a_3(ioff-1)= input a_3(n-1)
c output a_3(ioff)= input a_3(n)
c for ioff<0:
c output a_3(1)= input a_3(1-ioff)
c output a_3(2)= input a_3(2-ioff)
c ... ...
c output a_3(n+ioff-1)= input a_3(n-1)
c output a_3(n+ioff)= input a_3(n)
c output a_3(n+ioff+1)= input a_3(1)
c output a_3(n+ioff+2)= input a_3(2)
c ... ...
c output a_3(n-1)= input a_3(-ioff-1)
c output a_3(n)= input a_3(-ioff)
c
c istd stride of values in a, that is, length of dimensions
c of a before the one of length n
c
c n2 length of dimensions of a after the one of length n
c
c ws double precision ws_1(n) of working space
c*/
/*c
c internal variables
c*/
long i, i2, j, joff;
/*-----implicit-declarations-----*/
/*-----end-of-declarations-----*/
if (ioff == 0) goto L_100;
if (ioff < 0) goto L_50;
joff= n-ioff;
for (i2=1 ; i2<=n2 ; i2+=1) {
for (i=1 ; i<=istd ; i+=1) {
for (j=1 ; j<=joff ; j+=1) {
ws_1(j+ioff)= a_3(i, j, i2);
}
for (j=1 ; j<=ioff ; j+=1) {
ws_1(j)= a_3(i, j+joff, i2);
}
for (j=1 ; j<=n ; j+=1) {
a_3(i, j, i2)= ws_1(j);
}
}
}
goto L_100;
L_50:
joff= n+ioff;
for (i2=1 ; i2<=n2 ; i2+=1) {
for (i=1 ; i<=istd ; i+=1) {
for (j=1 ; j<=-ioff ; j+=1) {
ws_1(j+joff)= a_3(i, j, i2);
}
for (j=1 ; j<=joff ; j+=1) {
ws_1(j)= a_3(i, j-ioff, i2);
}
for (j=1 ; j<=n ; j+=1) {
a_3(i, j, i2)= ws_1(j);
}
}
}
L_100:
return;
}
