1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
|
#include <R.h>
#include <Rmath.h>
void lossdistrib(double *p, int *np, double *S, double *lu, double *q) {
/* recursive algorithm with first order correction for computing
the loss distribution.
p vector of default probabilities
np length of p
S vector of severities (should be same length as p)
lu loss unit
q the loss distribution */
int i, j, N, d1, d2;
double d, p1, p2, sum;
double *q1, *q2;
N = ceil(1./(*lu) + 1);
q1 = malloc( N * sizeof(double));
q2 = malloc( N * sizeof(double));
q[0] = 1;
for(i=0; i<(*np); i++){
d = S[i]/(*np * (*lu));
d1 = floor(d);
d2 = ceil(d);
p1 = p[i] * (d2-d);
p2 = p[i] - p1;
for(j=0; j<d1; j++){
q1[j]=0;
};
for(j=0; j<N-d1; j++){
q1[d1+j] = p1*q[j];
};
for(j=0; j<d2; j++){
q2[j]=0;
};
for(j=0; j<N-d2; j++){
q2[d2+j] = p2*q[j];
};
for(j=0; j<N; j++){
q[j] = q1[j] + q2[j] + (1-p[i]) * q[j];
};
}
/* correction for weight loss */
sum = 0;
for(j=0; j<N; j++){
sum += q[j];
}
q[N-1] += 1-sum;
free(q1);
free(q2);
}
void lossdistrib2( double *p, int *np, double *S, double *lu, double *q) {
/* recursive algorithm with first order correction
computes jointly the loss and recovery distribution
p vector of default probabilities
np length of p
S vector of severities (should be same length as p)
lu loss unit
q the joint probability distribution */
int i, j, k, l, m, n, N;
double x, y, sum;
double alpha1, alpha2, beta1, beta2;
double w1, w2, w3, w4;
double *qtemp;
N = ceil(1./(*lu) + 1);
qtemp = malloc( N * N * sizeof(double));
q[0] = 1;
for(k=0; k<(*np); k++){
x = S[k]/(*np * (*lu));
y = (1-S[k])/(*np * (*lu));
i = floor(x);
j = floor(y);
alpha1 = i + 1 - x;
alpha2 = 1 - alpha1;
beta1 = j + 1 - y;
beta2 = 1 - beta1;
w1 = alpha1 * beta1;
w2 = alpha1 * beta2;
w3 = alpha2 * beta2;
w4 = alpha2 * beta1;
/* init qtemp to 0 */
for(l=0; l < N*N; l++){
qtemp[l] = 0;
}
for(m=i; m<N; m++){
for(n=j; n<N; n++){
qtemp[m+N*n]+= w1 * p[k]* q[(m-i)+ N*(n-j)];
}
}
for(m=i; m<N; m++){
for(n=j+1; n<N; n++){
qtemp[m+N*n]+= w2 * p[k]* q[(m-i)+ N*(n-j-1)];
}
}
for(m=i+1; m<N; m++){
for(n=j+1; n<N; n++){
qtemp[m+N*n]+= w3 * p[k]* q[(m-i-1)+ N*(n-j-1)];
}
}
for(m=i+1; m<N; m++){
for(n=j; n<N; n++){
qtemp[m+N*n]+= w4 * p[k]* q[(m-i-1)+ N*(n-j)];
}
}
for(m=0; m<N; m++){
for(n=0; n<N;n++){
q[m+N*n] = (1-p[k]) * q[m+N*n]+ qtemp[m+N*n];
}
}
}
/* correction for weight loss */
sum = 0;
for(l=0; l<N*N; l++){
sum+=q[l];
}
q[N * N -1]+=1-sum;
free(qtemp);
}
double shockprob(double p, double rho, double Z, int give_log){
return( pnorm( (qnorm(p, 0, 1, 1, 0) -sqrt(rho) * Z)/sqrt(1 - rho), 0, 1, 1, give_log));
}
double shockseverity(double S, double Z, double rho, double p){
return( exp(shockprob(S * p, rho, Z, 1) - shockprob(p, rho, Z, 1)) );
}
void addandmultiply(double *X, double alpha, double *Y, int n) {
int i;
for(i = 0; i<n; i++){
Y[i] += alpha*X[i];
}
}
void BClossdist(double *SurvProb, int *dim1, int *dim2, double *recov, double *Z, double *w, int *n, double *rho, double *lu, double *L, double *R) {
int t, i, j, N;
double g;
double *gshocked, *Rshocked, *Sshocked, *Lw, *Rw;
gshocked = calloc((*dim1), sizeof(double));
Rshocked = calloc((*dim1), sizeof(double));
Sshocked = calloc((*dim1), sizeof(double));
N = ceil(1. / (*lu) + 1);
Lw = malloc(N * sizeof(double));
Rw = malloc(N * sizeof(double));
for(t=0; t < (*dim2); t++) {
for(i=0; i < *n; i++){
for(j=0; j < (*dim1); j++){
g = 1 - SurvProb[j + (*dim1) * t];
gshocked[j] = shockprob(g, *rho, Z[i], 0);
Sshocked[j] = shockseverity(1-recov[j], Z[i], *rho, g);
Rshocked[j] = 1 - Sshocked[j];
}
/* reset Lw and Rw to 0 */
for(j=0; j<N; j++){
Lw[j]=0;
Rw[j]=0;
}
lossdistrib(gshocked, dim1, Sshocked, lu, Lw);
lossdistrib(gshocked, dim1, Rshocked, lu, Rw);
addandmultiply(Lw, w[i], L + t * N, N);
addandmultiply(Rw, w[i], R + t * N, N);
}
}
free(gshocked);
free(Rshocked);
free(Sshocked);
free(Lw);
free(Rw);
}
|
