-
Notifications
You must be signed in to change notification settings - Fork 11
/
Copy pathexprtk_jump_diffusion_process.cpp
143 lines (120 loc) · 6.27 KB
/
exprtk_jump_diffusion_process.cpp
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
/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Merton Jump Diffusion Process Option Pricing Model *
* Author: Arash Partow (1999-2024) *
* URL: https://www.partow.net/programming/exprtk/index.html *
* *
* Copyright notice: *
* Free use of the Mathematical Expression Toolkit Library is *
* permitted under the guidelines and in accordance with the *
* most current version of the MIT License. *
* https://www.opensource.org/licenses/MIT *
* SPDX-License-Identifier: MIT *
* *
**************************************************************
*/
#include <cstdio>
#include <string>
#include "exprtk.hpp"
template <typename T>
void european_option_merton_jump_diffusion_process()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> parser_t;
typedef exprtk::function_compositor<T> compositor_t;
typedef typename compositor_t::function function_t;
const std::string european_option_merton_jump_diffusion_process_program =
" var lambda_t := lambda * t; "
" var v_sqr := v^2; "
" var sigmaJ_sqr := sigmaJ^2; "
" "
" var option_price := 0; "
" var factorial := 1; "
" "
" for (var i := 0; i < n; i += 1) "
" { "
" var prob := exp(-lambda_t) * lambda_t^i / factorial; "
" var r_i := r - lambda * muJ + (i / t) * log(1 + muJ); "
" var sigma_i := sqrt(v_sqr + (i * sigmaJ_sqr) / t); "
" "
" option_price += "
" switch "
" { "
" case callput_flag == 'call' : prob * bsm_call(s, k, r_i, t, sigma_i); "
" case callput_flag == 'put' : prob * bsm_put (s, k, r_i, t, sigma_i); "
" }; "
" "
" factorial *= (i > 1) ? i : 1; "
" }; "
" "
" option_price; ";
T s = T(100.00); // Spot / Stock / Underlying / Base price
T k = T(110.00); // Strike price
T v = T( 0.30); // Volatility
T t = T( 2.22); // Years to maturity
T r = T( 0.05); // Risk free rate
T lambda = T(0.0001); // Jump intensity (average jumps per year)
T muJ = T( -0.05); // Mean jump size (negative for downward jumps)
T sigmaJ = T( 0.30); // Standard deviation of the jump size
T n = T( 50.00); // Number of terms in the Poisson sum
std::string callput_flag;
symbol_table_t symbol_table(symbol_table_t::e_immutable);
symbol_table.add_variable ("s" , s );
symbol_table.add_variable ("k" , k );
symbol_table.add_variable ("v" , v );
symbol_table.add_variable ("t" , t );
symbol_table.add_variable ("r" , r );
symbol_table.add_variable ("lambda", lambda);
symbol_table.add_variable ("muJ" , muJ );
symbol_table.add_variable ("sigmaJ", sigmaJ);
symbol_table.add_variable ("n" , n );
symbol_table.add_stringvar("callput_flag",callput_flag);
symbol_table.add_pi();
compositor_t compositor(symbol_table);
compositor.add(
function_t("bsm_call")
.vars("s", "k", "r", "t", "v")
.expression
(
" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" var d2 := d1 - v * sqrt(t); "
" s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); "
));
compositor.add(
function_t("bsm_put")
.vars("s", "k", "r", "t", "v")
.expression
(
" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" var d2 := d1 - v * sqrt(t); "
" k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); "
));
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(european_option_merton_jump_diffusion_process_program, expression);
callput_flag = "call";
const T jdp_call_option_price = expression.value();
callput_flag = "put";
const T jdp_put_option_price = expression.value();
printf("JDPPrice(%4s, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
callput_flag.c_str(),
s, k, t, r, v,
jdp_call_option_price);
printf("JDPPrice(%4s, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
callput_flag.c_str(),
s, k, t, r, v,
jdp_put_option_price);
const T put_call_parity_diff =
(jdp_call_option_price - jdp_put_option_price) -
(s - k * std::exp(-r * t));
printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff);
}
int main()
{
european_option_merton_jump_diffusion_process<double>();
return 0;
}