Complex gamgamgamgam_mmpp(int i1,int i2,int i3,int i4) {
return spa(i1,i2)*spa(i1,i2)*spa(i1,i2)/spa(i2,i3)/spa(i3,i4)/spa(i4,i1) * (
0.5 * sij(i2,i3)/pow(sij(i1,i2),3) * ( pow(sij(i1,i3),2) + pow(sij(i2,i3),2) )
* ( pow(Clog(sij(i1,i3),sij(i2,i3)),2) + PISQ )
+ sij(i2,i3)/sij(i1,i2)/sij(i1,i2) * (sij(i1,i3)-sij(i2,i3))
* ( Clog(sij(i1,i3),sij(i2,i3)) )
+ sij(i2,i3)/sij(i1,i2) ) ; }
static double charact_funct1(double uu)
{
double a,b,rs,rsp,sig,tau,tpf1,tpf2, f10, c0, d0;
dcomplex g,z,w,tp1,tp2,DD,CN,ans,d,expo;
tau=T;
a=k*teta;
rs=rho*sigma;
rsp=rs*uu;
sig=sigma*sigma;
b=k+lambda-rs;
if(uu==0)
{
if(b==0)
{
c0=a*T*T/4.0;
d0=T/2.0;
}
else
{
c0=0.5*a*(exp(-b*T)+b*T - 1.0)/b/b;
d0=0.5*(1.0-exp(-b*T))/b;
}
f10=log(S/K)+(r-divid)*T+c0+d0*v;
return f10;
}
z=Complex(-b,rsp);
z=Cmul(z,z);
w=RCmul(sig,Complex(-uu*uu,uu));
d=Csqrt(Csub(z,w));
tp1=Complex(d.r+b,d.i-rsp);
tp2=Complex(-d.r+b,-d.i-rsp);
g=Cdiv(tp2,tp1);
expo=Cexp(RCmul(-tau,d));
DD=Csub(Complex(1,0),expo);
DD=Cdiv(DD,Csub(Complex(1,0),Cmul(g,expo)));
DD=Cmul(DD,RCmul(1.0/sig,tp2));
CN=Csub(Cmul(g,expo), Complex(1,0));
CN=Cdiv(CN,Csub(g, Complex(1,0) ));
tpf1=a*(tau*tp2.r-2.0*Clog(CN).r)/sig;
tpf2=a*(tau*tp2.i-2.0*Clog(CN).i)/sig;
tpf2+=(r-divid)*uu*tau;
ans=Complex(tpf1+v*DD.r,tpf2+v*DD.i+uu*log(S));
ans=Cmul(Cexp(ans),Cexp(Complex(0,-uu*log(K))));
ans=Cdiv(ans,Complex(0,uu));
return ans.r;
}
///******************* Gamma-OU 1d Model*******************///
void phi_psi_gou1d(PnlVect *ModelParams, double t, dcomplex u, dcomplex *phi_i, dcomplex *psi_i)
{
double lambda, alpha, beta;
double a_t;
dcomplex z0, z1, z2, z3;
lambda = GET(ModelParams, 1);
alpha = GET(ModelParams, 2);
beta = GET(ModelParams, 3);
a_t = exp(-lambda*t);
z0 = RCmul(a_t, u);
z1 = RCsub(alpha, z0);
z2 = RCsub(alpha, u);
z3 = RCmul(beta, Clog(Cdiv(z1, z2)));
*phi_i = z3;
*psi_i = z0;
}
void phi_psi_cir1d(PnlVect *ModelParams, double t, dcomplex u, dcomplex *phi_i, dcomplex *psi_i)
{
double lambda, theta, eta, SQR_eta;
dcomplex z1, z2;
double b_t, a_t;
//x0 = GET(ModelParams, 0);
lambda = GET(ModelParams, 1);
theta = GET(ModelParams, 2);
eta = GET(ModelParams, 3);
SQR_eta = SQR(eta);
a_t = exp(-lambda*t);
if (lambda == 0.) b_t = t;
else b_t = (1.-a_t)/lambda;
z1 = RCsub(1., RCmul(2*SQR_eta*b_t, u));
*phi_i = RCmul(-lambda*theta/(2*SQR_eta), Clog(z1));
z1 = RCmul(a_t, u);
z2 = RCsub(1., RCmul(2*SQR_eta*b_t, u));
*psi_i = Cdiv(z1, z2);
}
static double charact_func(double k)
{
double X,tau,roeps,u,b,I,eps,eps2;
dcomplex Ak,Bk,Ck,Dk,Lambdak,z1,z2,z3,zeta,psi_moins,psi_plus,expo,ans;
dcomplex dlk;
tau = T;
eps = sigma;
roeps = rho*eps;
X = log(S/K) + (r - divid)*tau;
eps2 = eps*eps;
if(func_type==1)
{
u = 1.;
b = kappa - roeps;
I = 1.;
}
else if(func_type==2)
{
u = -1.;
b = kappa;
I = 0.;
}
else
{
printf("erreur : dans charact_func il faut initialiser func_type a 1 ou 2.\n");
exit(-1);
}
if(heston==1)
{
z1 = Complex(k*k,-u*k);
z2 = Complex(b,-roeps*k);
z2 = Cmul(z2,z2);
zeta = Cadd(z2,RCmul(eps2,z1));
zeta = Csqrt(zeta);
psi_moins = Complex(b,-roeps*k);
psi_plus = RCmul(-1.,psi_moins);
psi_moins = Cadd(psi_moins,zeta);
psi_plus = Cadd(psi_plus,zeta);
expo = Cexp( RCmul(-tau,zeta) );
z3 = Cadd( psi_moins , Cmul(psi_plus,expo) );
Bk = RCmul(-1.,z1);
Bk = Cmul( Bk , Csub(Complex(1.,0),expo) );
Bk = Cdiv(Bk,z3);
Ak = Cdiv( z3 , RCmul(2.,zeta) );
Ak = Clog(Ak);
if(initlog>0)
{
dlk = Csub(Ak,lk_1);
if(dlk.i < -M_PI)
{
bk = bk + 1;
}
else if(dlk.i > M_PI)
{
bk = bk - 1;
}
initlog++;
lk_1 = Ak;
} else {
initlog++;
lk_1 = Ak;
}
Ak = Cadd(Ak, Complex(0.,2*M_PI*bk));
Ak = RCmul( 2. , Ak );
Ak = Cadd( RCmul(tau,psi_plus) , Ak);
Ak = RCmul( -kappa*teta/eps2 , Ak);
}
else
{
Ak = Complex(0.,0.);
Bk = Complex( -0.5*tau*k*k , 0.5*tau*u*k );
}
if(merton==1)
{
z1 = Complex( -0.5*v*v*k*k + I*(m0+0.5*v*v) , (m0+I*v*v)*k );
z1 = Cexp(z1);
z2 = Complex(I,k);
z2 = RCmul( exp(m0+0.5*v*v) -1, z2);
z2 = Cadd( Complex(1.,0.) , z2 );
Lambdak = Csub(z1,z2);
Ck = Complex(0.,0.);
Dk = RCmul(tau,Lambdak);
}
else
{
Ck = Complex(0.,0.);
Dk = Complex(0.,0.);
}
ans = Cadd( Ak , RCmul(V0,Bk) );
ans = Cadd( ans , Ck );
ans = Cadd( ans , RCmul(lambda0,Dk) );
ans = Cadd( ans , Complex(0.,k*X) );
ans = Cexp(ans);
ans = Cdiv(ans,Complex(0.,k));
return ans.r;
}
static double charact_func0(double k)
{
double X,tau,roeps,u,eps,eps2;
dcomplex Ak,Bk,Ck,Dk,Lambdak,z1,z2,z3,zeta,psi_moins,psi_plus,expo,ans;
dcomplex dlk;
tau = T;
eps = sigma;
roeps = rho*eps;
X = log(S/K) + (r - divid)*tau;
u = kappa - roeps/2.;
eps2 = eps*eps;
if(heston==1)
{
zeta.r = k*k*eps2*(1.-rho*rho) + u*u + eps2/4.;
zeta.i = 2.*k*roeps*u;
zeta = Csqrt(zeta);
psi_moins = Complex(u,roeps*k);
psi_plus = RCmul(-1.,psi_moins);
psi_moins = Cadd(psi_moins,zeta);
psi_plus = Cadd(psi_plus,zeta);
expo = Cexp( RCmul(-tau,zeta) );
z3 = Cadd( psi_moins , Cmul(psi_plus,expo) );
Bk = RCmul( -(k*k+0.25) , Csub(Complex(1.,0),expo) );
Bk = Cdiv(Bk,z3);
Ak = Cdiv( z3 , RCmul(2.,zeta) );
Ak = Clog(Ak);
if(initlog>0)
{
dlk = Csub(Ak,lk_1);
if(dlk.i < -M_PI)
{
bk = bk + 1;
}
else if(dlk.i > M_PI)
{
bk = bk - 1;
}
initlog++;
lk_1 = Ak;
} else {
initlog++;
lk_1 = Ak;
}
Ak = Cadd(Ak, Complex(0.,2*M_PI*bk));
Ak = RCmul( 2. , Ak );
Ak = Cadd( RCmul(tau,psi_plus) , Ak);
Ak = RCmul( -kappa*teta/eps2 , Ak);
}
else
{
Ak = Complex(0.,0.);
Bk = Complex( -0.5*tau*(k*k+0.25) ,0.);
}
if(merton==1)
{
z1 = Complex( 0.5*m0-0.5*v*v*(k*k-0.25) , -k*(m0+0.5*v*v) );
z1 = Cexp(z1);
z2 = Complex(0.5,-k);
z2 = RCmul( exp(m0+0.5*v*v) - 1. , z2);
z2 = Cadd( Complex(1.,0.) , z2 );
Lambdak = Csub(z1,z2);
Ck = Complex(0.,0.);
Dk = RCmul(tau,Lambdak);
}
else
{
Ck = Complex(0.,0.);
Dk = Complex(0.,0.);
}
ans = Cadd( Ak , RCmul(V0,Bk) );
ans = Cadd( ans , Ck );
ans = Cadd( ans , RCmul(lambda0,Dk) );
ans = Cadd( ans , RCmul(X,Complex(0.5,-k) ) );
ans = Cexp(ans);
ans = Cdiv(ans,Complex(k*k+0.25,0.));
if(probadelta == 1)
{
ans = Cmul( ans , Complex(0.5,-k) );
ans = RCmul( 1./S , ans );
}
return ans.r;
}
