Complete all Greek calculations for BS and MC, add README
This commit is contained in:
Kevin Keogh
42
Makefile
42
Makefile
@@ -1,35 +1,47 @@
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CC=gcc
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WINDOWS_CC=x86_64-w64-mingw32-gcc
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CFLAGS=-Wall -fPIC -O3 -ansi -pedantic-errors
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WINDOWS_CFLAGS= -Wall -O3 -ansi -pedantic-errors
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LDFLAGS=-lm
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PREFIX= /usr/local
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opt-pricer : src/opt-pricer.c gbm.o black_scholes.o utils.o
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WINDOWS_CC=x86_64-w64-mingw32-gcc
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WINDOWS_CFLAGS= -Wall -O3 -ansi -pedantic-errors
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WINDOWS_PLATFORM= windows
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.DEFAULT_GOAL := build/opt-pricer
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build/opt-pricer : src/opt-pricer.c build/depends/linux/gbm.o build/depends/linux/black_scholes.o build/depends/linux/utils.o
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@$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@
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gbm.o : src/gbm_mc.c
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build/depends/%/gbm.o : src/gbm_mc.c | folders
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@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
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black_scholes.o : src/black_scholes.c
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build/depends/%/black_scholes.o : src/black_scholes.c | folders
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@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
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utils.o : src/utils.c
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build/depends/%/utils.o : src/utils.c | folders
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@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
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strptime.o : src/strptime.c
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build/depends/%/strptime.o : src/strptime.c | folders
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@$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
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opt-pricer.exe : CC=$(WINDOWS_CC)
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opt-pricer.exe : CFLAGS=$(WINDOWS_CFLAGS)
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opt-pricer.exe : src/opt-pricer.c gbm.o black_scholes.o utils.o strptime.o
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@$(WINDOWS_CC) $(WINDOWS_CFLAGS) $^ $(LDFLAGS) -o $@
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folders:
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@mkdir -p build
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@mkdir -p build/depends
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@mkdir -p build/depends/linux
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@mkdir -p build/depends/windows
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build/opt-pricer.exe : CC=$(WINDOWS_CC)
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build/opt-pricer.exe : CFLAGS=$(WINDOWS_CFLAGS)
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build/opt-pricer.exe : src/opt-pricer.c build/depends/windows/gbm.o build/depends/windows/black_scholes.o build/depends/windows/utils.o build/depends/windows/strptime.o
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@$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@
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.PHONY: windows
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windows: opt-pricer.exe
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windows: build/opt-pricer.exe
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.PHONY: install
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install : opt-pricer
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install : build/opt-pricer
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@mkdir -p $(DESTDIR)$(PREFIX)/bin
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@cp $< $(DESTDIR)$(PREFIX)/bin/opt-pricer
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@rm -f $<
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@@ -40,4 +52,6 @@ uninstall :
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.PHONY: clean
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clean :
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@rm -f gbm.o black_scholes.o utils.o strptime.o
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@rm -rf build
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@mkdir build
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@mkdir build/depends
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12
README
Normal file
12
README
Normal file
@@ -0,0 +1,12 @@
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Demonstration of a black-scholes model in C
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Note that there are two models, a pure Monte Carlo implementation
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and the closed form black scholes equation.
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Recommended number of simulations is 100,000,000 for Gamma convergence, the
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other Greeks converge by 1,000,000.
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TODO:
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1. Find a C implementation for Sobol sequence so that Gamma convergence
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is faster
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2. Tests...
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@@ -22,5 +22,9 @@ void bsm(struct Option *opt)
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price = opt->spot * normalcdf(d1 * opt->type) * opt->type - opt->strike *
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exp(-opt->rfr * tte) * normalcdf(d2 * opt->type) * opt->type;
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opt->fv = price;
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opt->vega = opt->spot / 100 * exp(-opt->rfr * tte) * pow(tte, 0.5) * normalpdf(d1);
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opt->delta = (opt->type == 1) ? normalcdf(d1) : normalcdf(d1) - 1;
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opt->gamma = 1 / (opt->spot * opt->vol * pow(tte, 0.5)) * normalcdf(d1);
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opt->vega = opt->spot / 100 * pow(tte, 0.5) * normalpdf(d1);
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opt->rho = opt->type * tte * opt->strike * exp(-opt->rfr * tte) * normalcdf(opt->type * d2) / 100;
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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));
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}
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45
src/gbm_mc.c
45
src/gbm_mc.c
@@ -19,9 +19,10 @@ double gbm_simulation(double spot, double rfr, double vol, double tte, double ra
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void gbm(struct Option *opt)
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{
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double tte, expiry_date, value_date, level, rand;
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double tte, theta_tte, expiry_date, value_date, level, rand, df;
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double delta_shift = 0, vega_shift = 0, theta_shift = 0, rho_shift = 0;
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double price, delta, vega, theta, rho;
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double gamma_shift = 0, base_gamma = 0, upper_gamma = 0, lower_gamma = 0;
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double price, delta, gamma, vega, theta, rho;
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double base = 0;
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int i;
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@@ -30,30 +31,52 @@ void gbm(struct Option *opt)
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expiry_date = mktime(opt->expiry_date);
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value_date = mktime(opt->value_date);
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tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365);
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theta_tte = tte - 1. / 365;
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for (i=0; i<opt->sims; i++) {
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rand = gaussrand();
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/* Base scenario */
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level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand);
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base += max((level - opt->strike) * opt->type, 0);
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level = gbm_simulation(opt->spot + 1, opt->rfr, opt->vol, tte, rand);
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/* Delta scenario */
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level = gbm_simulation(opt->spot + 0.0001, opt->rfr, opt->vol, tte, rand);
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delta_shift += max((level - opt->strike) * opt->type, 0);
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level = gbm_simulation(opt->spot, opt->rfr, opt->vol + 0.01, tte, rand);
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/* Gamma scenario */
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upper_gamma = gbm_simulation(opt->spot + 0.00001, opt->rfr, opt->vol, tte, rand);
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base_gamma = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte, rand);
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lower_gamma = gbm_simulation(opt->spot - 0.00001, opt->rfr, opt->vol, tte, rand);
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gamma_shift += (max((upper_gamma - opt->strike) * opt->type, 0) -
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2 * max((base_gamma - opt->strike) * opt->type, 0) +
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max((lower_gamma - opt->strike) * opt->type, 0)) /
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pow(0.00001, 2);
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/* Vega scenario */
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level = gbm_simulation(opt->spot, opt->rfr, opt->vol + 0.0001, tte, rand);
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vega_shift += max((level - opt->strike) * opt->type, 0);
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level = gbm_simulation(opt->spot, opt->rfr, opt->vol, tte - 1./365., rand);
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/* Theta scenario */
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level = gbm_simulation(opt->spot, opt->rfr, opt->vol, theta_tte, rand);
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theta_shift += max((level - opt->strike) * opt->type, 0);
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/* Rho scenario */
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level = gbm_simulation(opt->spot, opt->rfr + 0.01, opt->vol, tte, rand);
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rho_shift += max((level - opt->strike) * opt->type, 0);
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}
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price = base / opt->sims * 1 / pow((1 + opt->rfr), tte);
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delta = delta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
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vega = vega_shift / opt->sims * 1 / pow((1 + opt->rfr), tte);
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df = 1 / pow((1 + opt->rfr), tte);
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price = base / opt->sims * df;
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delta = delta_shift / opt->sims * df;
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gamma = gamma_shift / opt->sims * df;
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vega = vega_shift / opt->sims * df;
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theta = theta_shift / opt->sims * 1 / pow((1 + opt->rfr), tte - 1./365.);
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rho = rho_shift / opt->sims * 1 / pow((1 + opt->rfr + 0.01), tte);
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opt->fv = price;
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opt->delta = (delta - price);
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opt->vega = (vega - price);
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opt->theta = (theta - price);
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opt->delta = (delta - price) / 0.0001;
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opt->gamma = gamma;
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opt->vega = (vega - price) / 0.01;
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opt->theta = (theta - price) / (tte - theta_tte);
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opt->rho = (rho - price);
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}
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@@ -8,6 +8,7 @@
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#include "strptime.h"
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#endif
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#include <locale.h>
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#include <stdio.h>
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#include <string.h>
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#include <time.h>
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@@ -70,6 +71,12 @@ int print_help(void)
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}
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char* read_type(struct Option opt)
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{
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return (opt.type == 1) ? "Call" : "Put";
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}
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int main(int argc, char *argv[])
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{
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double spot = 0, strike = 0, rfr = 0, vol = 0, sims = 1000;
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@@ -158,41 +165,42 @@ int main(int argc, char *argv[])
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strftime(value_date, 11, "%Y-%m-%d", &value);
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bsm(&bs_opt);
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gbm(&mc_opt);
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setlocale(LC_ALL,"");
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printf(
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"\nValuation date: %s\n\n"
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" | BS Analytic | BS Monte Carlo |\n"
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" ---------------------------------------------\n"
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" |Type: | %10.1i | %13.1i |\n"
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" |Type: | %10s | %13s |\n"
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" |Spot: | %10.2f | %13.2f |\n"
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" |Expiry: | %s | %s |\n"
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" |Strike: | %10.2f | %13.2f |\n"
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" |Risk-free: | %10.2f%% | %13.2f%% |\n"
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" |Implied Vol:| %10.2f%% | %13.2f%% |\n"
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/*
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" |sims: | %4.2f| %4.2f|\n"
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" |exp: | %4.2s| %4.2f|\n"
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*/
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" ---------------------------------------------\n"
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" |Fair value: | %8.4f | %11.4f |\n"
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" |Delta: | %8.4f | %11.4f |\n"
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" |Vega: | %8.4f | %11.4f |\n"
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" |Theta: | %8.4f | %11.4f |\n"
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" |Rho: | %8.4f | %11.4f |\n",
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" |Gamma: | %8.4f | %11.4f |\n",
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value_date,
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bs_opt.type, mc_opt.type,
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read_type(bs_opt), read_type(mc_opt),
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bs_opt.spot, mc_opt.spot,
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expiry_date, expiry_date,
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bs_opt.strike, mc_opt.strike,
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bs_opt.rfr*100, mc_opt.rfr*100,
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bs_opt.vol*100, mc_opt.vol*100,
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bs_opt.fv, mc_opt.fv,
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bs_opt.delta, mc_opt.delta,
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bs_opt.gamma, mc_opt.gamma);
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printf(
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" |Vega: | %8.4f | %11.4f |\n"
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" |Theta: | %8.4f | %11.4f |\n"
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" |Rho: | %8.4f | %11.4f |\n"
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" |Simulations:| | %'11ld |\n"
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" ---------------------------------------------\n\n",
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bs_opt.vega, mc_opt.vega,
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bs_opt.theta, mc_opt.theta,
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bs_opt.rho, mc_opt.rho);
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printf(
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" ---------------------------------------------\n\n"
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);
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/*
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printf("%s", buffer1);
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printf("%s", buffer2);
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*/
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bs_opt.rho, mc_opt.rho,
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mc_opt.sims);
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return 0;
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}
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