kevindkeogh/opt-pricer
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Complete all Greek calculations for BS and MC, add README

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This commit is contained in:
Kevin Keogh
2017-07-27 23:01:03 -04:00
parent 785c546ba3
commit a28df367bf
5 changed files with 104 additions and 43 deletions
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42
Makefile
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@@ -1,35 +1,47 @@
CC=gcc CC=gcc
WINDOWS_CC=x86_64-w64-mingw32-gcc
CFLAGS=-Wall -fPIC -O3 -ansi -pedantic-errors CFLAGS=-Wall -fPIC -O3 -ansi -pedantic-errors
WINDOWS_CFLAGS= -Wall -O3 -ansi -pedantic-errors
LDFLAGS=-lm LDFLAGS=-lm
PREFIX= /usr/local PREFIX= /usr/local
opt-pricer : src/opt-pricer.c gbm.o black_scholes.o utils.o WINDOWS_CC=x86_64-w64-mingw32-gcc
WINDOWS_CFLAGS= -Wall -O3 -ansi -pedantic-errors
WINDOWS_PLATFORM= windows
.DEFAULT_GOAL := build/opt-pricer
build/opt-pricer : src/opt-pricer.c build/depends/linux/gbm.o build/depends/linux/black_scholes.o build/depends/linux/utils.o
@$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@ @$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@
gbm.o : src/gbm_mc.c build/depends/%/gbm.o : src/gbm_mc.c | folders
@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@ @$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
black_scholes.o : src/black_scholes.c build/depends/%/black_scholes.o : src/black_scholes.c | folders
@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@ @$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
utils.o : src/utils.c build/depends/%/utils.o : src/utils.c | folders
@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@ @$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
strptime.o : src/strptime.c build/depends/%/strptime.o : src/strptime.c | folders
@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@ @$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
opt-pricer.exe : CC=$(WINDOWS_CC) folders:
opt-pricer.exe : CFLAGS=$(WINDOWS_CFLAGS) @mkdir -p build
opt-pricer.exe : src/opt-pricer.c gbm.o black_scholes.o utils.o strptime.o @mkdir -p build/depends
@$(WINDOWS_CC) $(WINDOWS_CFLAGS) $^ $(LDFLAGS) -o $@ @mkdir -p build/depends/linux
@mkdir -p build/depends/windows
build/opt-pricer.exe : CC=$(WINDOWS_CC)
build/opt-pricer.exe : CFLAGS=$(WINDOWS_CFLAGS)
build/opt-pricer.exe : src/opt-pricer.c build/depends/windows/gbm.o build/depends/windows/black_scholes.o build/depends/windows/utils.o build/depends/windows/strptime.o
@$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@
.PHONY: windows .PHONY: windows
windows: opt-pricer.exe windows: build/opt-pricer.exe
.PHONY: install .PHONY: install
install : opt-pricer install : build/opt-pricer
@mkdir -p $(DESTDIR)$(PREFIX)/bin @mkdir -p $(DESTDIR)$(PREFIX)/bin
@cp $< $(DESTDIR)$(PREFIX)/bin/opt-pricer @cp $< $(DESTDIR)$(PREFIX)/bin/opt-pricer
@rm -f $< @rm -f $<
@@ -40,4 +52,6 @@ uninstall :
.PHONY: clean .PHONY: clean
clean : clean :
@rm -f gbm.o black_scholes.o utils.o strptime.o @rm -rf build
@mkdir build
@mkdir build/depends

12
README Normal file
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@@ -0,0 +1,12 @@
Demonstration of a black-scholes model in C
Note that there are two models, a pure Monte Carlo implementation
and the closed form black scholes equation.
Recommended number of simulations is 100,000,000 for Gamma convergence, the
other Greeks converge by 1,000,000.
TODO:
1. Find a C implementation for Sobol sequence so that Gamma convergence
is faster
2. Tests...

6
src/black_scholes.c
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@@ -22,5 +22,9 @@ void bsm(struct Option *opt)
price = opt->spot * normalcdf(d1 * opt->type) * opt->type - opt->strike * price = opt->spot * normalcdf(d1 * opt->type) * opt->type - opt->strike *
exp(-opt->rfr * tte) * normalcdf(d2 * opt->type) * opt->type; exp(-opt->rfr * tte) * normalcdf(d2 * opt->type) * opt->type;
opt->fv = price; opt->fv = price;
opt->vega = opt->spot / 100 * exp(-opt->rfr * tte) * pow(tte, 0.5) * normalpdf(d1); opt->delta = (opt->type == 1) ? normalcdf(d1) : normalcdf(d1) - 1;
opt->gamma = 1 / (opt->spot * opt->vol * pow(tte, 0.5)) * normalcdf(d1);
opt->vega = opt->spot / 100 * pow(tte, 0.5) * normalpdf(d1);
opt->rho = opt->type * tte * opt->strike * exp(-opt->rfr * tte) * normalcdf(opt->type * d2) / 100;
opt->theta = -opt->type * (opt->rfr * opt->strike * exp(-opt->rfr * tte) * normalcdf(opt->type * d2)) - (opt->vol / (2 * pow(tte, 0.5)) * opt->spot * normalpdf(opt->type * d1));
} }

45
src/gbm_mc.c
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@@ -19,9 +19,10 @@ double gbm_simulation(double spot, double rfr, double vol, double tte, double ra
void gbm(struct Option *opt) void gbm(struct Option *opt)
{ {
double tte, expiry_date, value_date, level, rand; double tte, theta_tte, expiry_date, value_date, level, rand, df;
double delta_shift = 0, vega_shift = 0, theta_shift = 0, rho_shift = 0; double delta_shift = 0, vega_shift = 0, theta_shift = 0, rho_shift = 0;
double price, delta, vega, theta, rho; double gamma_shift = 0, base_gamma = 0, upper_gamma = 0, lower_gamma = 0;
double price, delta, gamma, vega, theta, rho;
double base = 0; double base = 0;
int i; int i;
@@ -30,30 +31,52 @@ void gbm(struct Option *opt)
expiry_date = mktime(opt->expiry_date); expiry_date = mktime(opt->expiry_date);
value_date = mktime(opt->value_date); value_date = mktime(opt->value_date);
tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365); tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365);
theta_tte = tte - 1. / 365;
for (i=0; i<opt->sims; i++) { for (i=0; i<opt->sims; i++) {
rand = gaussrand(); rand = gaussrand();
/* Base scenario */
level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand); level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand);
base += max((level - opt->strike) * opt->type, 0); base += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot + 1, opt->rfr, opt->vol, tte, rand);
/* Delta scenario */
level = gbm_simulation(opt->spot + 0.0001, opt->rfr, opt->vol, tte, rand);
delta_shift += max((level - opt->strike) * opt->type, 0); delta_shift += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot, opt->rfr, opt->vol + 0.01, tte, rand);
/* Gamma scenario */
upper_gamma = gbm_simulation(opt->spot + 0.00001, opt->rfr, opt->vol, tte, rand);
base_gamma = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand);
lower_gamma = gbm_simulation(opt->spot - 0.00001, opt->rfr, opt->vol, tte, rand);
gamma_shift += (max((upper_gamma - opt->strike) * opt->type, 0) -
2 * max((base_gamma - opt->strike) * opt->type, 0) +
max((lower_gamma - opt->strike) * opt->type, 0)) /
pow(0.00001, 2);
/* Vega scenario */
level = gbm_simulation(opt->spot, opt->rfr, opt->vol + 0.0001, tte, rand);
vega_shift += max((level - opt->strike) * opt->type, 0); vega_shift += max((level - opt->strike) * opt->type, 0);
level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte - 1./365., rand);
/* Theta scenario */
level = gbm_simulation(opt->spot, opt->rfr, opt->vol, theta_tte, rand);
theta_shift += max((level - opt->strike) * opt->type, 0); theta_shift += max((level - opt->strike) * opt->type, 0);
/* Rho scenario */
level = gbm_simulation(opt->spot, opt->rfr + 0.01, opt->vol, tte, rand); level = gbm_simulation(opt->spot, opt->rfr + 0.01, opt->vol, tte, rand);
rho_shift += max((level - opt->strike) * opt->type, 0); rho_shift += max((level - opt->strike) * opt->type, 0);
} }
price = base / opt->sims * 1 / pow((1 + opt->rfr), tte); df = 1 / pow((1 + opt->rfr), tte);
delta = delta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte); price = base / opt->sims * df;
vega = vega_shift / opt->sims * 1 / pow((1 + opt->rfr), tte); delta = delta_shift / opt->sims * df;
gamma = gamma_shift / opt->sims * df;
vega = vega_shift / opt->sims * df;
theta = theta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte - 1./365.); theta = theta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte - 1./365.);
rho = rho_shift / opt->sims * 1 / pow((1 + opt->rfr + 0.01), tte); rho = rho_shift / opt->sims * 1 / pow((1 + opt->rfr + 0.01), tte);
opt->fv = price; opt->fv = price;
opt->delta = (delta - price); opt->delta = (delta - price) / 0.0001;
opt->vega = (vega - price); opt->gamma = gamma;
opt->theta = (theta - price); opt->vega = (vega - price) / 0.01;
opt->theta = (theta - price) / (tte - theta_tte);
opt->rho = (rho - price); opt->rho = (rho - price);
} }

42
src/opt-pricer.c
View File

@@ -8,6 +8,7 @@
#include "strptime.h" #include "strptime.h"
#endif #endif
#include <locale.h>
#include <stdio.h> #include <stdio.h>
#include <string.h> #include <string.h>
#include <time.h> #include <time.h>
@@ -70,6 +71,12 @@ int print_help(void)
} }
char* read_type(struct Option opt)
{
return (opt.type == 1) ? "Call" : "Put";
}
int main(int argc, char *argv[]) int main(int argc, char *argv[])
{ {
double spot = 0, strike = 0, rfr = 0, vol = 0, sims = 1000; double spot = 0, strike = 0, rfr = 0, vol = 0, sims = 1000;
@@ -158,41 +165,42 @@ int main(int argc, char *argv[])
strftime(value_date, 11, "%Y-%m-%d", &value); strftime(value_date, 11, "%Y-%m-%d", &value);
bsm(&bs_opt); bsm(&bs_opt);
gbm(&mc_opt); gbm(&mc_opt);
setlocale(LC_ALL,"");
printf( printf(
"\nValuation date: %s\n\n" "\nValuation date: %s\n\n"
" | BS Analytic | BS Monte Carlo |\n" " | BS Analytic | BS Monte Carlo |\n"
" ---------------------------------------------\n" " ---------------------------------------------\n"
" |Type: | %10.1i | %13.1i |\n" " |Type: | %10s | %13s |\n"
" |Spot: | %10.2f | %13.2f |\n" " |Spot: | %10.2f | %13.2f |\n"
" |Expiry: | %s | %s |\n"
" |Strike: | %10.2f | %13.2f |\n" " |Strike: | %10.2f | %13.2f |\n"
" |Risk-free: | %10.2f%% | %13.2f%% |\n" " |Risk-free: | %10.2f%% | %13.2f%% |\n"
" |Implied Vol:| %10.2f%% | %13.2f%% |\n" " |Implied Vol:| %10.2f%% | %13.2f%% |\n"
/* " ---------------------------------------------\n"
" |sims: | %4.2f| %4.2f|\n"
" |exp: | %4.2s| %4.2f|\n"
*/
" |Fair value: | %8.4f | %11.4f |\n" " |Fair value: | %8.4f | %11.4f |\n"
" |Delta: | %8.4f | %11.4f |\n" " |Delta: | %8.4f | %11.4f |\n"
" |Vega: | %8.4f | %11.4f |\n" " |Gamma: | %8.4f | %11.4f |\n",
" |Theta: | %8.4f | %11.4f |\n"
" |Rho: | %8.4f | %11.4f |\n",
value_date, value_date,
bs_opt.type, mc_opt.type, read_type(bs_opt), read_type(mc_opt),
bs_opt.spot, mc_opt.spot, bs_opt.spot, mc_opt.spot,
expiry_date, expiry_date,
bs_opt.strike, mc_opt.strike, bs_opt.strike, mc_opt.strike,
bs_opt.rfr*100, mc_opt.rfr*100, bs_opt.rfr*100, mc_opt.rfr*100,
bs_opt.vol*100, mc_opt.vol*100, bs_opt.vol*100, mc_opt.vol*100,
bs_opt.fv, mc_opt.fv, bs_opt.fv, mc_opt.fv,
bs_opt.delta, mc_opt.delta, bs_opt.delta, mc_opt.delta,
bs_opt.gamma, mc_opt.gamma);
printf(
" |Vega: | %8.4f | %11.4f |\n"
" |Theta: | %8.4f | %11.4f |\n"
" |Rho: | %8.4f | %11.4f |\n"
" |Simulations:| | %'11ld |\n"
" ---------------------------------------------\n\n",
bs_opt.vega, mc_opt.vega, bs_opt.vega, mc_opt.vega,
bs_opt.theta, mc_opt.theta, bs_opt.theta, mc_opt.theta,
bs_opt.rho, mc_opt.rho); bs_opt.rho, mc_opt.rho,
printf( mc_opt.sims);
" ---------------------------------------------\n\n"
);
/*
printf("%s", buffer1);
printf("%s", buffer2);
*/
return 0; return 0;
} }