def analy(self,N_o): ''' Analytical solution ''' # --- portfolio loss distribution @ t = \tau via analytical formulas --- opt_val = lambda S: 5.*bp.blsprice(S,self.K,self.rfr,self.T-self.tau,self.sigma,'put') \ + 10.*bp.dnOutCall(S,self.K,self.rfr,self.T-self.tau,self.sigma,self.H) #ran1 = npr.multivariate_normal(np.zeros(self.D),np.eye(self.D),N_o) #ran1 = npr.standard_normal((N_o,self.D)) ran1 = norm(loc=0,scale=1).ppf(lhs(self.D,samples=N_o)) S1 = np.zeros((N_o,self.D)) S1[:,:] = self.S0 S1[:,:] = S1[:,:] * np.exp((self.mu - 0.5 * self.sigma**2) * self.tau\ + self.sigma * np.sqrt(self.tau) * ran1[:,:]) ValueTau = np.zeros(N_o) for n in range(N_o): for d in range(self.D): ValueTau[n] += -opt_val(S1[n,d]) + S1[n,d] * self.delta[d] L_analy = np.sort(self.Value0 - ValueTau) #L_analy = np.sort(-ValueTau + self.Value0 * np.exp(self.rfr*self.tau)) print L_analy var = scs.scoreatpercentile(L_analy, self.perc*100.) eel = np.mean(np.maximum(L_analy-var,0)) return (var, eel)
from scipy import linalg import tools_benchmark as fun from tools_doe import trans import doe_lhs # Initialization of the problem dim = 10 ndoe = 10 * dim # Upper and lower bounds of the problem xlimits = np.zeros((dim, 2)) xlimits[:, 0] = -10 xlimits[:, 1] = 10 # Construction of the DOE in [0,1] xt = doe_lhs.lhs(dim, ndoe, 'm') # Transform the DOE in [LB,UB] xt = trans(xt, xlimits[:, 0], xlimits[:, 1]) # Compute the output (+ the gradient) yt, yd = fun.carre(xt) # Construction of the validation points ntest = 500 xtest = doe_lhs.lhs(dim, ntest) xtest = trans(xtest, xlimits[:, 0], xlimits[:, 1]) ytest, ydtest = fun.carre(xtest) ########### The LS model
import MOE.function as fct
import numpy as np
import csv
import doe_lhs as doe
func = lambda x:fct.test_1D(x)
dim = 1
n_train = 20
## Training points
Max = 1*np.ones(dim)
Min = 0*np.ones(dim)
X_train = doe.lhs(dim,samples=n_train)
X_train = doe.lhs_maximinESE(X_train)
for i in range(len(X_train)):
for j in range(len(X_train[0])):
X_train[i][j] = Min[j]+X_train[i][j]*(Max[j]-Min[j])
print i
Y_train = func(X_train)
fichier = open("DONNEES/test_1D_20.csv",'a')
csvwriter = csv.writer(fichier)
val = np.c_[X_train,Y_train]
csvwriter.writerows(val)
fichier.close()