-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathbasic.cpp
More file actions
262 lines (253 loc) · 15.1 KB
/
Copy pathbasic.cpp
File metadata and controls
262 lines (253 loc) · 15.1 KB
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
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
#include "basic.h"
namespace GBM {
namespace MC {
namespace Direct {
std::vector<double> call_price(double &S_0, double &K, double &r, double &sigma, double &T, int &M) {
std::clock_t t = clock();
double sum_price = 0.;
double sum_2_price = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
sum_price += D * std::max(S_T - K, 0.);
sum_2_price += std::pow(D * std::max(S_T - K, 0.), 2);
}
double m = sum_price / (double) M;
double v = ((1 / (double) M) * sum_2_price - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_delta(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_S) {
std::clock_t t = clock();
double sum_delta = 0.;
double sum_2_delta = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_m = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_h = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double price_m = D * std::max(S_T_m - K, 0.);
double price_h = D * std::max(S_T_h - K, 0.);
sum_delta += (price_h - price_m) / (2 * d_S);
sum_2_delta += std::pow((price_h - price_m) / (2 * d_S), 2);
}
double m = (sum_delta) / (double) M;
double v = ((1 / (double) M) * sum_2_delta - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_gamma(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_S) {
std::clock_t t = clock();
double sum_gamma = 0.;
double sum_2_gamma = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_l = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_m = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_h = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double price_l = D * std::max(S_T_l - K, 0.);
double price_m = D * std::max(S_T_m - K, 0.);
double price_h = D * std::max(S_T_h - K, 0.);
sum_gamma += (price_h - 2 * price_m + price_l) / (d_S * d_S);
sum_2_gamma += std::pow((price_h - 2 * price_m + price_l) / (d_S * d_S), 2);
}
double m = (sum_gamma) / (double) M;
double v = ((1 / (double) M) * sum_2_gamma - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_vega(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_sigma) {
std::clock_t t = clock();
double sum_vega = 0.;
double sum_2_vega = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_m = S_0 * exp(T * (r - 0.5 * (sigma - d_sigma) * (sigma - d_sigma)) + (sigma - d_sigma) * sqrt(T) * W);
double S_T_h = S_0 * exp(T * (r - 0.5 * (sigma + d_sigma) * (sigma + d_sigma)) + (sigma + d_sigma) * sqrt(T) * W);
double price_m = D * std::max(S_T_m - K, 0.);
double price_h = D * std::max(S_T_h - K, 0.);
sum_vega += (price_h - price_m) / (2*d_sigma);
sum_2_vega += std::pow((price_h - price_m) / d_sigma, 2);
}
double m = (sum_vega) / (double) M;
double v = ((1 / (double) M) * sum_2_vega - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
}
namespace Antithetic {
std::vector<double> call_price(double &S_0, double &K, double &r, double &sigma, double &T, int &M) {
std::clock_t t = clock();
double sum_price = 0.;
double sum_2_price = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_1 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_2 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
sum_price += D * (std::max(S_T_1 - K, 0.) + std::max(S_T_2 - K, 0.)) / 2;
sum_2_price += std::pow(D * (std::max(S_T_1 - K, 0.) + std::max(S_T_2 - K, 0.)) / 2, 2);
}
double m = sum_price / (double) M;
double v = ((1 / (double) M) * sum_2_price - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_delta(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_S) {
std::clock_t t = clock();
double sum_delta = 0.;
double sum_2_delta = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_m_1 = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_h_1 = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_m_2 = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double S_T_h_2 = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double price_m_1 = D * std::max(S_T_m_1 - K, 0.);
double price_h_1 = D * std::max(S_T_h_1 - K, 0.);
double price_m_2 = D * std::max(S_T_m_2 - K, 0.);
double price_h_2 = D * std::max(S_T_h_2 - K, 0.);
sum_delta += ((price_h_1 - price_m_1) / (2 * d_S) + (price_h_2 - price_m_2) / (2 * d_S)) / 2;
sum_2_delta += std::pow(((price_h_1 - price_m_1) / (2 * d_S) + (price_h_2 - price_m_2) / (2 * d_S)) / 2, 2);
}
double m = (sum_delta) / (double) M;
double v = ((1 / (double) M) * sum_2_delta - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_gamma(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_S) {
std::clock_t t = clock();
double sum_gamma = 0.;
double sum_2_gamma = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_l_1 = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_m_1 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_h_1 = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_l_2 = (S_0 - d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double S_T_m_2 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double S_T_h_2 = (S_0 + d_S) * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double price_l_1 = D * std::max(S_T_l_1 - K, 0.);
double price_m_1 = D * std::max(S_T_m_1 - K, 0.);
double price_h_1 = D * std::max(S_T_h_1 - K, 0.);
double price_l_2 = D * std::max(S_T_l_2 - K, 0.);
double price_m_2 = D * std::max(S_T_m_2 - K, 0.);
double price_h_2 = D * std::max(S_T_h_2 - K, 0.);
sum_gamma += ((price_h_1 - 2 * price_m_1 + price_l_1) / (d_S * d_S) + (price_h_2 - 2 * price_m_2 + price_l_2) / (d_S * d_S)) / 2;
sum_2_gamma += std::pow(((price_h_1 - 2 * price_m_1 + price_l_1) / (d_S * d_S) + (price_h_2 - 2 * price_m_2 + price_l_2) / (d_S * d_S)) / 2, 2);
}
double m = (sum_gamma) / (double) M;
double v = ((1 / (double) M) * sum_2_gamma - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
std::vector<double>
call_vega(double &S_0, double &K, double &r, double &sigma, double &T, int &M, double &d_sigma) {
std::clock_t t = clock();
double sum_vega = 0.;
double sum_2_vega = 0.;
double D = exp(-r * T);
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double S_T_m_1 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double S_T_h_1 = S_0 * exp(T * (r - 0.5 * (sigma + d_sigma) * (sigma + d_sigma)) + (sigma + d_sigma) * sqrt(T) * W);
double S_T_m_2 = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * (-W));
double S_T_h_2 = S_0 * exp(T * (r - 0.5 * (sigma + d_sigma) * (sigma + d_sigma)) + (sigma + d_sigma) * sqrt(T) * (-W));
double price_m_1 = D * std::max(S_T_m_1 - K, 0.);
double price_h_1 = D * std::max(S_T_h_1 - K, 0.);
double price_m_2 = D * std::max(S_T_m_2 - K, 0.);
double price_h_2 = D * std::max(S_T_h_2 - K, 0.);
sum_vega += ((price_h_1 - price_m_1) / d_sigma + (price_h_2 - price_m_2) / d_sigma) / 2;
sum_2_vega += std::pow(((price_h_1 - price_m_1) / d_sigma + (price_h_2 - price_m_2) / d_sigma) / 2, 2);
}
double m = (sum_vega) / (double) M;
double v = ((1 / (double) M) * sum_2_vega - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration};
return res;
}
}
namespace ControlVariate {
std::vector<double> call_price(double &S_0, double &K, double &r, double &sigma, double &T, int &M) {
std::clock_t t = clock();
//pilot simulation
double rho = 0.;//correlation between Y and Z, just for information
double c = 0.;
int p = 1000;
double D = exp(-r * T);
double E_Y = 0.;
double E_Y_2 = 0.;
std::vector<double> V_Y;
std::vector<double> V_Z;
double Var_Z = 0.;
//generate Y and Z samples
for (int i(0); i<p; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double X = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
V_Y.push_back(D * std::max(X - K, 0.));
V_Z.push_back(D * X);
E_Y += V_Y[i] / p;
E_Y_2 += std::pow(V_Y[i], 2) / p;
Var_Z += std::pow((V_Z[i] - S_0), 2) / p;
}
for (int i(0); i<p; ++i) {
c += - (V_Y[i] - E_Y) * (V_Z[i] - S_0) / (p*Var_Z);
rho += (V_Y[i] - E_Y) * (V_Z[i] - S_0) / (p*sqrt(Var_Z * (E_Y_2 - std::pow(E_Y, 2))));
}
double sum_price = 0.;
double sum_2_price = 0.;
for (int i = 0; i < M; ++i) {
double X_1 = (double) rand() / RAND_MAX;
double X_2 = (double) rand() / RAND_MAX;
double W = sqrt(-2 * log(X_1)) * sin(2 * M_PI * X_2);
double X = S_0 * exp(T * (r - 0.5 * sigma * sigma) + sigma * sqrt(T) * W);
double Y = D * std::max(X - K, 0.);
double Z = D * X;
double theta_c = Y + c*(Z - S_0);
sum_price += theta_c;
sum_2_price += std::pow(theta_c, 2);
}
double m = sum_price / (double) M;
double v = ((1 / (double) M) * sum_2_price - m * m) / (double) M;
double duration = (std::clock() - t) / (double) CLOCKS_PER_SEC;
std::vector<double> res = {m, 1.96*sqrt(v / M), duration, rho};
return res;
}
}
}
}