/*We use the Cauchy Gourat theorem to compute the derivatives of the double(Mellin+Laplace) transform */ static dcomplex dermellin(dcomplex l, double sg, double r, int nummom) { dcomplex term, cv, mu; int i; double r0,sumr, sumi/*,x[NPOINTS_FUSAITAGL+1],w[NPOINTS_FUSAITAGL+1]*/; double v; double *x,*w; x=malloc((NPOINTS_FUSAITAGL+1)*sizeof(double)); w=malloc((NPOINTS_FUSAITAGL+1)*sizeof(double)); sumr=0.0; sumi=0.0; gauleg(0, 2*M_PI, x, w,NPOINTS_FUSAITAGL); v = 2*r/(sg*sg)-1.0; cv = Complex(v,0.0); mu = Csqrt(Cadd(Complex(v*v,0), RCmul(2.0,l))); r0 = Creal(RCmul(0.5,Csub(mu,cv))); if(r0>1.0) r0=0.25; for (i=1;i<=NPOINTS_FUSAITAGL;i++) { term = RCmul(pow(r0,nummom), Cexp(Complex(0.0, nummom*x[i]))); sumr += w[i]*Creal(Cdiv(mellintransform(l, RCmul(r0, Cexp(Complex(0.0, x[i]))), sg, r), term)); sumi += w[i]*Cimag(Cdiv(mellintransform(l, RCmul(r0, Cexp(Complex(0.0, x[i]))), sg, r), term)); } free(x); free(w); return Complex(exp(factln(nummom))*sumr/(2.0*M_PI),exp(factln(nummom))*sumi/(2.0*M_PI)); }
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; }
void ComplexLUBackSubst(pcomplex **a, int n, int *indx, pcomplex *b) { int i, ip, j, ii = -1; pcomplex sum; for (i = 0; i < n; i++) { ip = indx[i]; sum = b[ip]; b[ip] = b[i]; if (ii >= 0) { for (j = ii; j <= i - 1; j++) sum = Csub(sum, Cmul(a[i][j], b[j])); } else if ((sum.re != 0.0) || (sum.im != 0.0)) ii = i; b[i] = sum; } for (i = n - 1; i >= 0; i--) { sum = b[i]; for (j = i + 1; j < n; j++) sum = Csub(sum, Cmul(a[i][j], b[j])); b[i] = Cdiv(sum, a[i][i]); } }
/*Computation the double(Mellin+Laplace) transform of the density of arithmetic average */ static dcomplex mellintransform(dcomplex l, dcomplex n, double sg, double r) { dcomplex mu,nterm1, nterm2, nterm3, dterm1, dterm2; dcomplex num, den, cv,cost; double v; v= 2*r/(sg*sg)-1.0; cv =Complex(v,0.0); mu = Csqrt(Cadd(Complex(v*v,0), RCmul(2.0,l))); cost=RCmul(log(2.0/(sg*sg)), n); nterm1 =Clgamma(Cadd(n,CONE)); nterm2 =Clgamma(Cadd(RCmul(0.5, Cadd(mu,cv)),CONE)); nterm3 =Clgamma(Csub(RCmul(0.5, Csub(mu,cv)),n)); num = Cadd(Cadd( nterm1,nterm2),nterm3); dterm1 =Clgamma(RCmul(0.5, Csub(mu,cv))); dterm2 =Clgamma(Cadd(Cadd(RCmul(0.5, Cadd(mu,cv)),CONE),n)); den = Cadd( dterm1,dterm2); return Cdiv(Cexp(Cadd(Csub(num,den),cost)),l); }
void fixrts(float d[], int m) { void zroots(fcomplex a[], int m, fcomplex roots[], int polish); int i,j,polish; fcomplex a[NMAX],roots[NMAX]; a[m]=ONE; for (j=m-1;j>=0;j--) a[j]=Complex(-d[m-j],0.0); polish=1; zroots(a,m,roots,polish); for (j=1;j<=m;j++) if (Cabs(roots[j]) > 1.0) roots[j]=Cdiv(ONE,Conjg(roots[j])); a[0]=Csub(ZERO,roots[1]); a[1]=ONE; for (j=2;j<=m;j++) { a[j]=ONE; for (i=j;i>=2;i--) a[i-1]=Csub(a[i-2],Cmul(roots[j],a[i-1])); a[0]=Csub(ZERO,Cmul(roots[j],a[0])); } for (j=0;j<=m-1;j++) d[m-j] = -a[j].r; }
void hypser(fcomplex a, fcomplex b, fcomplex c, fcomplex z, fcomplex *series, fcomplex *deriv) { void nrerror(char error_text[]); int n; fcomplex aa,bb,cc,fac,temp; deriv->r=0.0; deriv->i=0.0; fac=Complex(1.0,0.0); temp=fac; aa=a; bb=b; cc=c; for (n=1;n<=1000;n++) { fac=Cmul(fac,Cmul(aa,Cdiv(bb,cc))); deriv->r+=fac.r; deriv->i+=fac.i; fac=Cmul(fac,RCmul(1.0/n,z)); *series=Cadd(temp,fac); if (series->r == temp.r && series->i == temp.i) return; temp= *series; aa=Cadd(aa,ONE); bb=Cadd(bb,ONE); cc=Cadd(cc,ONE); } nrerror("convergence failure in hypser"); }
void hypdrv(float s, float yy[], float dyyds[]) { fcomplex z,y[3],dyds[3]; y[1]=Complex(yy[1],yy[2]); y[2]=Complex(yy[3],yy[4]); z=Cadd(z0,RCmul(s,dz)); dyds[1]=Cmul(y[2],dz); dyds[2]=Cmul(Csub(Cmul(Cmul(aa,bb),y[1]),Cmul(Csub(cc, Cmul(Cadd(Cadd(aa,bb),ONE),z)),y[2])), Cdiv(dz,Cmul(z,Csub(ONE,z)))); dyyds[1]=dyds[1].r; dyyds[2]=dyds[1].i; dyyds[3]=dyds[2].r; dyyds[4]=dyds[2].i; }
///******************* 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); }
void frenel(float x, float *s, float *c) { void nrerror(char error_text[]); int k,n,odd; float a,ax,fact,pix2,sign,sum,sumc,sums,term,test; fcomplex b,cc,d,h,del,cs; ax=fabs(x); if (ax < sqrt(FPMIN)) { *s=0.0; *c=ax; } else if (ax <= XMIN) { sum=sums=0.0; sumc=ax; sign=1.0; fact=PIBY2*ax*ax; odd=TRUE; term=ax; n=3; for (k=1;k<=MAXIT;k++) { term *= fact/k; sum += sign*term/n; test=fabs(sum)*EPS; if (odd) { sign = -sign; sums=sum; sum=sumc; } else { sumc=sum; sum=sums; } if (term < test) break; odd=!odd; n += 2; } if (k > MAXIT) nrerror("series failed in frenel"); *s=sums; *c=sumc; } else { pix2=PI*ax*ax; b=Complex(1.0,-pix2); cc=Complex(1.0/FPMIN,0.0); d=h=Cdiv(ONE,b); n = -1; for (k=2;k<=MAXIT;k++) { n += 2; a = -n*(n+1); b=Cadd(b,Complex(4.0,0.0)); d=Cdiv(ONE,Cadd(RCmul(a,d),b)); cc=Cadd(b,Cdiv(Complex(a,0.0),cc)); del=Cmul(cc,d); h=Cmul(h,del); if (fabs(del.r-1.0)+fabs(del.i) < EPS) break; } if (k > MAXIT) nrerror("cf failed in frenel"); h=Cmul(Complex(ax,-ax),h); cs=Cmul(Complex(0.5,0.5), Csub(ONE,Cmul(Complex(cos(0.5*pix2),sin(0.5*pix2)),h))); *c=cs.r; *s=cs.i; } if (x < 0.0) { *c = -(*c); *s = -(*s); } }
int CarrMethod_VectStrike(PnlVect *K, PnlVect * Price, double S0, double T, double B, double CallPut, double r, double divid, double sigma, void * Model, dcomplex (*ln_phi)(dcomplex u,double t,void * model)) { int n; dcomplex dzeta,dzetaBS; double alpha=0.75; int Nlimit = 4*2048;//2048; //>> Should be even => use of real_fft //number of integral discretization steps double mone;//0.010; double Kstep=B*2/(Nlimit); // strike domain is (-B,B) double h = M_2PI/(Nlimit*Kstep); //double B = 0.5*(Nlimit)*Kstep; // strike domain is (-B,B) double vn = 0; dcomplex vn_minus_alpha_plus_uno = Complex(0,-(alpha+1)); dcomplex i_vn_plus_alpha = Complex(alpha,0); dcomplex uno_plus_alpha_plus_ivn =Complex(1+alpha,vn); PnlVectComplex * y = pnl_vect_complex_create(Nlimit); // Should become output pnl_vect_resize(K,Nlimit); pnl_vect_resize(Price,Nlimit); //delta mone=1; //printf("limit integration %7.4f \n",A); for(n=0; n<Nlimit; n++) { dzeta = Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,vn*B)); dzetaBS = Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,vn*B)); dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS)); dzeta = Cdiv(dzeta,i_vn_plus_alpha); dzeta = Cdiv(dzeta,uno_plus_alpha_plus_ivn); //>> With Simson rules pnl_vect_complex_set(y,n,RCmul(3+mone-((n==0)?1:0),Conj(dzeta))); //>> Update value vn += h; vn_minus_alpha_plus_uno.r+=h; i_vn_plus_alpha.i+=h; uno_plus_alpha_plus_ivn.i+=h; mone*=-1; } pnl_ifft_inplace(y); for(n=0;n<Nlimit;n++) { LET(K,n)=exp(-B+n*Kstep+(r-divid)*T)*(S0); pnl_cf_call_bs(S0,GET(K,n),T,r,divid,sigma,&LET(Price,n),&vn); LET(Price,n)+=2./3* S0/(Kstep)*exp(alpha*(B-n*Kstep)-divid*T)*GET_REAL(y,n); } if (CallPut==2) for(n=0;n<Nlimit;n++) LET(Price,n)-=S0*exp(-divid*T)+GET(K,n)*exp(-r*T); /* printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-5),GET(Price,Nlimit/2-5)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-4),GET(Price,Nlimit/2-4)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-3),GET(Price,Nlimit/2-3)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-2),GET(Price,Nlimit/2-2)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-1),GET(Price,Nlimit/2-1)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+0),GET(Price,Nlimit/2+0)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+1),GET(Price,Nlimit/2+1)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+2),GET(Price,Nlimit/2+2)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+3),GET(Price,Nlimit/2+3)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+4),GET(Price,Nlimit/2+4)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+5),GET(Price,Nlimit/2+5)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+6),GET(Price,Nlimit/2+6)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+7),GET(Price,Nlimit/2+7)); printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+8),GET(Price,Nlimit/2+8)); pnl_vect_free(&K); pnl_vect_free(&Price); */ return OK; }
int CarrMethod_old_verison(double S0, double T, double K, double CallPut, double r, double divid, double sigma, void * Model, dcomplex (*ln_phi)(dcomplex u,double t,void * model), double *ptprice, double *ptdelta) { int n; dcomplex dzeta,dzetaBS; double alpha=0.0; //taking account of dividends int Nlimit = 2048; //number of integral discretization steps double logstrikestep = 0.01; double k0 = log(K/(S0*exp(-divid*T))); double h = M_2PI/Nlimit/logstrikestep; //integral discretization step double A = (Nlimit-1)*h; // integration domain is (-A/2,A/2) PnlVectComplex * z =pnl_vect_complex_create(Nlimit); PnlVectComplex * y =pnl_vect_complex_create(Nlimit); double vn = -A/2; dcomplex vn_minus_alpha_plus_uno = Complex(-A/2,-(alpha+1)); dcomplex i_vn_plus_alpha = Complex(alpha,-A/2); double weight = 1./3; //Simpson's rule weights dcomplex uno_plus_alpha_plus_ivn=Complex(1+alpha,vn); //delta for(n=0; n<Nlimit; n++) { dzeta= Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,vn*(r*T-k0))); dzetaBS= Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,vn*(r*T-k0))); dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS)); dzeta = Cdiv(dzeta,i_vn_plus_alpha); dzeta = RCmul(weight,dzeta); pnl_vect_complex_set(z,n,dzeta); dzeta=Cdiv(dzeta,uno_plus_alpha_plus_ivn); pnl_vect_complex_set(y,n,dzeta); //>> Update value vn += h; vn_minus_alpha_plus_uno.r+=h; i_vn_plus_alpha.i+=h; uno_plus_alpha_plus_ivn.i+=h; weight = (weight<1) ? 4./3 : 2./3; //Simpson's rule weights weight = (n==(Nlimit-2)) ?2./3. :weight; } //pnl_vect_complex_print(z); pnl_fft_inplace(z); pnl_fft_inplace(y); //pnl_vect_complex_print(z); //Black-Scholes formula pnl_cf_call_bs(S0,K,T,r,divid,sigma,ptprice,ptdelta); S0 *= exp(-divid*T); /*Call Case*/ *ptprice += S0*A/M_2PI/(Nlimit-1)*exp(-alpha*k0)*GET_REAL(y,0); *ptdelta += exp(-divid*T)*(A/M_2PI/(Nlimit-1)*exp(-alpha*k0)*GET_REAL(z,0)); //Put Case via parity*/ if (CallPut==2) { *ptprice =*ptprice-S0+K*exp(-r*T); *ptdelta =*ptdelta-exp(-divid*T); } //memory desallocation pnl_vect_complex_free(&z); pnl_vect_complex_free(&y); return OK; }
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; }
void cisi(float x, float *ci, float *si) { void nrerror(char error_text[]); int i,k,odd; float a,err,fact,sign,sum,sumc,sums,t,term; fcomplex h,b,c,d,del; t=fabs(x); if (t == 0.0) { *si=0.0; *ci = -1.0/FPMIN; return; } if (t > TMIN) { b=Complex(1.0,t); c=Complex(1.0/FPMIN,0.0); d=h=Cdiv(ONE,b); for (i=2;i<=MAXIT;i++) { a = -(i-1)*(i-1); b=Cadd(b,Complex(2.0,0.0)); d=Cdiv(ONE,Cadd(RCmul(a,d),b)); c=Cadd(b,Cdiv(Complex(a,0.0),c)); del=Cmul(c,d); h=Cmul(h,del); if (fabs(del.r-1.0)+fabs(del.i) < EPS) break; } if (i > MAXIT) nrerror("cf failed in cisi"); h=Cmul(Complex(cos(t),-sin(t)),h); *ci = -h.r; *si=PIBY2+h.i; } else { if (t < sqrt(FPMIN)) { sumc=0.0; sums=t; } else { sum=sums=sumc=0.0; sign=fact=1.0; odd=TRUE; for (k=1;k<=MAXIT;k++) { fact *= t/k; term=fact/k; sum += sign*term; err=term/fabs(sum); if (odd) { sign = -sign; sums=sum; sum=sumc; } else { sumc=sum; sum=sums; } if (err < EPS) break; odd=!odd; } if (k > MAXIT) nrerror("maxits exceeded in cisi"); } *si=sums; *ci=sumc+log(t)+EULER; } if (x < 0.0) *si = -(*si); }
int ComplexLUDecompose(pcomplex **a, int n, double *vv, int *indx, double *pd) // pcomplex **a; the matrix whose LU-decomposition is wanted // int n; order of a // double *vv; work vector of size n (stores implicit // scaling of each row) // int *indx; => row permutation according to partial // pivoting sequence // double *pd; => 1 if number of row interchanges was even, // -1 if odd (NULL OK) { int i, imax, j, k; double big, dum, temp, d; pcomplex sum, cdum; d = 1.0; imax = 0; // only to shut the compiler up. for (i = 0; i < n; i++) { big = 0.0; for (j = 0; j < n; j++) { if ((temp = Cabs(a[i][j])) > big) big = temp; } if (big == 0.0) { printf("singular matrix in routine ComplexLUDecompose\n"); return 1; } vv[i] = 1.0 / big; } for (j = 0; j < n; j++) { for (i = 0; i < j; i++) { sum = a[i][j]; for (k = 0; k < i; k++) sum = Csub(sum, Cmul(a[i][k], a[k][j])); a[i][j] = sum; } big = 0.0; for (i = j; i < n; i++) { sum = a[i][j]; for (k = 0; k < j; k++) sum = Csub(sum, Cmul(a[i][k], a[k][j])); a[i][j] = sum; dum = vv[i] * Cabs(sum); if (dum >= big) { big = dum; imax = i; } } if (j != imax) { for (k = 0; k < n; k++) { cdum = a[imax][k]; a[imax][k] = a[j][k]; a[j][k] = cdum; } d = -d; vv[imax] = vv[j]; } indx[j] = imax; if (a[j][j].re == 0.0 && a[j][j].im == 0.0) a[j][j] = Complex(1.0e-20, 1.0e-20); if (j != n - 1){ cdum = Cdiv(Complex(1.0, 0.0), a[j][j]); for (i = j + 1; i < n; i++) a[i][j] = Cmul(a[i][j], cdum); } } if (pd != NULL) *pd = d; return 0; }
int CarrMethod(double S0, double T, double K, double CallPut, double r, double divid, double sigma, void * Model, dcomplex (*ln_phi)(dcomplex u,double t,void * model), double *ptprice, double *ptdelta) { int n; dcomplex dzeta,dzetaBS; double alpha=0.75; //taking account of dividends int Nlimit = 2048;//2048; //number of integral discretization steps double logstrikestep = 0.01; double k0 = log(K/S0)-(r-divid)*T; double h = M_PI/Nlimit/logstrikestep; //integral discretization step double z,y; double vn = 0; dcomplex vn_minus_alpha_plus_uno = Complex(0,-(alpha+1)); dcomplex i_vn_plus_alpha = Complex(alpha,0); double weight = 1./3; //Simpson's rule weights dcomplex uno_plus_alpha_plus_ivn=Complex(1+alpha,vn); //delta z=0;y=0; for(n=0; n<Nlimit; n++) { dzeta=Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,-vn*k0)); // printf("%7.4f + i %7.4f \n",dzeta.r,dzeta.i); dzetaBS= Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,-vn*k0)); dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS)); dzeta = Cdiv(dzeta,i_vn_plus_alpha); dzeta = RCmul(weight,dzeta); //printf(">>%7.4f + i %7.4f \n",dzeta.r,dzeta.i); z+=dzeta.r; dzeta=Cdiv(dzeta,uno_plus_alpha_plus_ivn); y+=dzeta.r; //>> Update value vn += h; vn_minus_alpha_plus_uno.r+=h; i_vn_plus_alpha.i+=h; uno_plus_alpha_plus_ivn.i+=h; weight = (weight<1) ? 4./3 : 2./3; //Simpson's rule weights weight = (n==(Nlimit-2)) ?2./3. :weight; } //Black-Scholes formula pnl_cf_call_bs(S0,K,T,r,divid,sigma,ptprice,ptdelta); S0 *= exp(-divid*T); /*Call Case*/ *ptprice += S0/(Nlimit*logstrikestep)*exp(-alpha*k0)*y; //*ptprice = y; *ptdelta += exp(-divid*T)/(Nlimit*logstrikestep)*exp(-alpha*k0)*z; //Put Case via parity*/ if (CallPut==2) { *ptprice =*ptprice-S0+K*exp(-r*T); *ptdelta =*ptdelta-exp(-divid*T); } //memory desallocation return OK; }
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; }