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Changes in progress, added calculations for FinDiff greeks

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This commit is contained in:
Kevin Keogh
2017-07-24 22:58:41 -04:00
parent 58d17adfa2
commit 15d750abf1
7 changed files with 186 additions and 99 deletions
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22
src/black_scholes.c
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@@ -5,20 +5,22 @@
#include <math.h>
#include <time.h>
double bsm(double spot, double rfr, double vol, double strike,
struct tm expiry, struct tm value, int type)
void bsm(struct Option *opt)
{
double d1, d2, tte, price;
time_t value_date, expiry_date;
expiry_date = mktime(&expiry);
value_date = mktime(&value);
expiry_date = mktime(opt->expiry_date);
value_date = mktime(opt->value_date);
tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365);
d1 = log(spot / strike) + tte * (rfr + pow(vol, 2) / 2)
/ (vol * pow(tte, 0.5));
d2 = d1 - (vol * pow(tte, 0.5));
price = spot * normalcdf(d1 * type) * type -
strike * exp(-rfr * tte) * normalcdf(d2 * type) * type;
return price;
d1 = (log(opt->spot / opt->strike) + tte * (opt->rfr + pow(opt->vol, 2) / 2))
/ (opt->vol * pow(tte, 0.5));
d2 = d1 - (opt->vol * pow(tte, 0.5));
price = opt->spot * normalcdf(d1 * opt->type) * opt->type - opt->strike *
exp(-opt->rfr * tte) * normalcdf(d2 * opt->type) * opt->type;
opt->fv = price;
opt->vega = opt->spot * exp(-opt->rfr * tte) * pow(tte, 0.5) * normalpdf(d1);
}

11
src/black_scholes.h
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@@ -1,14 +1,7 @@
#ifndef BLACK_SCHOLES_H_
#define BLACK_SCHOLES_H_
struct tm;
double gbm(double spot, double rfr, double vol, double strike, struct tm expiry,
struct tm value, int type, int sims);
double normalcdf(double value);
double bsm(double spot, double rfr, double vol, double strike, struct tm expiry,
struct tm value, int type);
struct Option;
void bsm(struct Option *option);
#endif

41
src/gbm_mc.c
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@@ -17,26 +17,43 @@ double gbm_simulation(double spot, double rfr, double vol, double tte, double ra
return spot * exp(drift + stoch);
}
double gbm(double spot, double rfr, double vol, double strike, struct tm expiry,
struct tm value, int type, int sims)
void gbm(struct Option *opt)
{
double tte, expiry_date, value_date, level, price, rand;
double results = 0;
double tte, expiry_date, value_date, level, rand;
double delta_shift = 0, vega_shift = 0, theta_shift = 0, rho_shift = 0;
double price, delta, vega, theta, rho;
double base = 0;
int i;
if (sims < 1) sims = 1;
if (opt->sims < 1) opt->sims = 1;
expiry_date = mktime(&expiry);
value_date = mktime(&value);
expiry_date = mktime(opt->expiry_date);
value_date = mktime(opt->value_date);
tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365);
for (i=0; i<sims; i++) {
for (i=0; i<opt->sims; i++) {
rand = gaussrand();
level = gbm_simulation(spot, rfr, vol, tte, rand);
results += max((level - strike) * type, 0);
level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand);
base += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot + 0.01, opt->rfr, opt->vol, tte, rand);
delta_shift += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot, opt->rfr, opt->vol + 0.01, tte, rand);
vega_shift += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte + 1/365, rand);
theta_shift += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot, opt->rfr + 0.0001, opt->vol, tte, rand);
rho_shift += max((level - opt->strike) * opt->type, 0);
}
price = results / sims * 1 / pow((1 + rfr), tte);
price = base / opt->sims * 1 / pow((1 + opt->rfr), tte);
delta = delta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
vega = vega_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
theta = theta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
rho = rho_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
return price;
opt->fv = price;
opt->delta = (delta - price) * 100 * opt->spot;
opt->vega = (vega - price) * opt->spot;
opt->theta = (theta - price) * opt->spot;
opt->rho = (rho - price) * opt->spot;
}

3
src/gbm_mc.h
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@@ -3,8 +3,9 @@
#include <time.h>
struct Option;
double gbm_simulation(double spot, double rfr, double vol, double tte, double rand);
double gbm(double spot, double rfr, double vol, double strike, struct tm expiry, struct tm value, int type, int sims);
void gbm(struct Option *opt);
#endif

172
src/opt-pricer.c
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@@ -2,6 +2,7 @@
#include "black_scholes.h"
#include "gbm_mc.h"
#include "utils.h"
#ifdef __MINGW32__
#include "strptime.h"
@@ -21,25 +22,25 @@ struct helptext {
static struct helptext options[] = {
{"-s, --spot",
"Spot price"},
"Spot price"},
{"-k, --strike",
"Strike price"},
"Strike price"},
{"-r, --rfr",
"Risk-free rate"},
"Risk-free rate"},
{"-v, --implied-volatility",
"Implied volatility"},
"Implied volatility"},
{"-d, --effective-date",
"Effective date [YYYY-MM-DD]"},
"Effective date [YYYY-MM-DD]"},
{"-e, --expiry-date",
"Expiry date [YYYY-MM-DD]"},
"Expiry date [YYYY-MM-DD]"},
{"-N",
"Number of MC simulations"},
"Number of MC simulations"},
{"-c, --call",
"Call flag"},
"Call flag"},
{"-p, --put",
"Put or call flag"},
"Put or call flag"},
{"-h, --help",
"This help text"},
"This help text"},
{ NULL , NULL }
};
@@ -72,59 +73,59 @@ int print_help(void)
int main(int argc, char *argv[])
{
double spot = 0, strike = 0, rfr = 0, vol = 0, sims = 1000;
double bs_price, mc_price;
char expiry_date[11], buffer[512];
char expiry_date[11], value_date[11], buffer[1024];
int opt, option_index = 0, type = 0;
struct tm expiry, value;
struct tm value, expiry;
struct Option bs_opt, mc_opt;
extern char *optarg;
extern int getopt();
extern char *optarg;
extern int getopt_long();
memset(&expiry, 0, sizeof(expiry));
memset(&value, 0, sizeof(value));
while ((opt = getopt_long(argc, argv, "s:k:r:v:d:e:N:cp:h", long_options, &option_index)) != -1) {
switch (opt) {
case 's':
if (sscanf(optarg, "%lf", &spot) == EOF) {
return 1;
};
break;
case 'k': /* strike */
if (sscanf(optarg, "%lf", &strike) == EOF) {
return 1;
};
break;
case 'r': /* risk-free rate */
if (sscanf(optarg, "%lf.", &rfr) == EOF) {
return 1;
};
break;
case 'v': /* implied volatility */
if (sscanf(optarg, "%lf", &vol) == EOF) {
return 1;
};
break;
case 'e': /* expiry date, must be YYYY-MM-DD */
strptime(optarg, "%Y-%m-%d", &expiry);
break;
case 'd': /* valuation date, must be YYYY-MM-DD */
strptime(optarg, "%Y-%m-%d", &value);
break;
case 'N': /* number of simulations */
if (sscanf(optarg, "%lf", &sims) == EOF) {
return 1;
};
break;
case 'c': /* set as call */
type = 1;
break;
case 'p': /* set as put */
type = -1;
break;
case 'h': /* print help*/
print_help();
return 0;
case 's':
if (sscanf(optarg, "%lf", &spot) == EOF) {
return 1;
};
break;
case 'k': /* strike */
if (sscanf(optarg, "%lf", &strike) == EOF) {
return 1;
};
break;
case 'r': /* risk-free rate */
if (sscanf(optarg, "%lf.", &rfr) == EOF) {
return 1;
};
break;
case 'v': /* implied volatility */
if (sscanf(optarg, "%lf", &vol) == EOF) {
return 1;
};
break;
case 'e': /* expiry date, must be YYYY-MM-DD */
strptime(optarg, "%Y-%m-%d", &expiry);
break;
case 'd': /* valuation date, must be YYYY-MM-DD */
strptime(optarg, "%Y-%m-%d", &value);
break;
case 'N': /* number of simulations */
if (sscanf(optarg, "%lf", &sims) == EOF) {
return 1;
};
break;
case 'c': /* set as call */
type = 1;
break;
case 'p': /* set as put */
type = -1;
break;
case 'h': /* print help*/
print_help();
return 0;
}
}
if (spot == 0 || strike == 0 || rfr == 0 || vol == 0) {
@@ -132,19 +133,56 @@ int main(int argc, char *argv[])
return 1;
}
bs_opt.spot = spot;
bs_opt.strike = strike;
bs_opt.expiry_date = &expiry;
bs_opt.value_date = &value;
bs_opt.rfr = rfr;
bs_opt.vol = vol;
bs_opt.type = type;
mc_opt.spot = spot;
mc_opt.strike = strike;
mc_opt.expiry_date = &expiry;
mc_opt.value_date = &value;
mc_opt.rfr = rfr;
mc_opt.vol = vol;
mc_opt.type = type;
mc_opt.sims = sims;
strftime(expiry_date, 11, "%Y-%m-%d", &expiry);
bs_price = bsm(spot, rfr, vol, strike, expiry, value, type);
mc_price = gbm(spot, rfr, vol, strike, expiry, value, type, sims);
sprintf(&buffer[0], "Arguments:\n"
"spot: %f\n"
"strike: %f\n"
"rfr: %f\n"
"vol: %f\n"
"sims: %f\n"
"exp: %s\n"
"BS price: %f\n"
"MC price: %f\n",
spot, strike, rfr, vol, sims, expiry_date, bs_price, mc_price);
strftime(value_date, 11, "%Y-%m-%d", &value);
bsm(&bs_opt);
gbm(&mc_opt);
sprintf(&buffer[0],
"\nValuation date: %s\n\n"
" | BS Analytic | BS Monte Carlo |\n"
" ---------------------------------------------\n"
" |Type: | %10.1i | %13.1i |\n"
" |Spot: | %10.2f | %13.2f |\n"
" |Strike: | %10.2f | %13.2f |\n"
" |Risk-free: | %10.2f%% | %13.2f%% |\n"
" |Implied Vol:| %10.2f%% | %13.2f%% |\n"
/*
" |sims: | %4.2f| %4.2f|\n"
" |exp: | %4.2s| %4.2f|\n"
*/
" |Fair value: | %10.2f | %13.2f |\n"
" |Delta: | %10.2f | %13.2f |\n"
" |Vega: | %10.2f | %13.2f |\n"
" |Theta: | %8.4f | %11.4f |\n"
" |Rho : | %8.4f | %11.4f |\n\n",
value_date,
bs_opt.type, mc_opt.type,
bs_opt.spot, mc_opt.spot,
bs_opt.strike, mc_opt.strike,
bs_opt.rfr*100, mc_opt.rfr*100,
bs_opt.vol*100, mc_opt.vol*100,
bs_opt.fv, mc_opt.fv,
bs_opt.delta, mc_opt.delta,
bs_opt.vega, mc_opt.vega,
bs_opt.theta, mc_opt.theta,
bs_opt.rho, mc_opt.rho);
printf("%s", buffer);
return 0;
}

12
src/utils.c
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@@ -1,5 +1,10 @@
#include <math.h>
#include <stdlib.h>
#include <time.h>
#define M_PI 3.14159265358979323846264338327950288
double normalcdf(double z)
{
@@ -23,6 +28,13 @@ double normalcdf(double z)
return 0.5 * (1 + sign * y);
}
double normalpdf(double z)
{
return exp(-0.5 * pow(z, 2)) / pow(M_PI * 2, 0.5);
}
double gaussrand()
{
/* Marsaglia and Bray, ``A Convenient Method for Generating Normal Variables'' */

24
src/utils.h
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@@ -3,6 +3,30 @@
double normalcdf(double z);
double normalpdf(double z);
double gaussrand();
struct Option {
/* option details */
int type;
double strike;
struct tm *expiry_date;
/* market data */
struct tm *value_date;
double spot;
double rfr;
double vol;
int sims;
/* fv and greeks */
double fv;
double delta;
double vega;
double rho;
double gamma;
double theta;
};
#endif