Initial commit

Makefile

@@ -0,0 +1,16 @@
+CC=gcc
+CFLAGS=-Wall -fPIC -O3 -ansi -pedantic-errors
+LDFLAGS=-lgsl -lcblas -lm
+
+pricer : src/optpricer.c gbm.o black_scholes.o
+	$(CC) $(CFLAGS) $^ $(LDFLAGS) -o $@
+
+gbm.o : src/gbm_mc.c
+	$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
+
+black_scholes.o : src/black_scholes.c
+	$(CC) $(CFLAGS) -c $^ $(LDFLAGS) -o $@
+
+.PHONY: clean
+clean:
+	rm -f gbm.o black_scholes.o

src/black_scholes.c

@@ -0,0 +1,32 @@
+#define _XOPEN_SOURCE
+
+#include "black_scholes.h"
+#include <cblas.h>
+#include <math.h>
+#include <stdio.h>
+#include <string.h>
+#include <time.h>
+#include <unistd.h>
+
+double normalcdf(double value)
+{
+	return 0.5 * erfc(-value * M_SQRT1_2);
+}
+
+double bsm(double spot, double rfr, double vol, double strike,
+		struct tm expiry, struct tm value, int type)
+{
+	double d1, d2, tte, price;
+	time_t value_date, expiry_date;
+
+	expiry_date = mktime(&expiry);
+	value_date = mktime(&value);
+	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;
+}

src/black_scholes.h

@@ -0,0 +1,14 @@
+#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);
+
+#endif

src/gbm_mc.c

@@ -0,0 +1,55 @@
+#define _XOPEN_SOURCE
+#define max(X,Y) (((X) > (Y)) ? (X) : (Y))
+
+#include <gsl/gsl_statistics_double.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <math.h>
+#include <time.h>
+#include "gbm_mc.h"
+
+double gbm_simulation(double spot, double rfr, double vol, double tte, double rand)
+{
+	double drift, stoch;
+	drift = (rfr - pow(vol, 2) / 2) * tte;
+	stoch = vol * pow(tte, 0.5) * rand;
+	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)
+{
+	const gsl_rng_type *T;
+	gsl_rng *r;
+	double tte, expiry_date, value_date, level, price;
+	double *rands, *results;
+	int i;
+
+	rands = (double *)malloc(sizeof(double) * sims);
+	results = (double *)malloc(sizeof(double) * sims);
+
+	expiry_date = mktime(&expiry);
+	value_date = mktime(&value);
+	tte = difftime(expiry_date, value_date) / (60 * 60 * 24 * 365);
+
+	/* get array of normal random numbers */
+	gsl_rng_env_setup();
+	T = gsl_rng_default;
+	r = gsl_rng_alloc(T);
+
+	for (i=0; i<sims; i++) {
+		rands[i] = gsl_ran_gaussian(r, 1);
+	}
+
+	for (i=0; i<sims; i++) {
+		level = gbm_simulation(spot, rfr, vol, tte, rands[i]);
+		results[i] = max((level - strike) * type, 0);
+	}
+
+	price = gsl_stats_mean(results, 1, sims) * 1 / pow((1 + rfr), tte);
+
+	gsl_rng_free(r);
+	free(rands);
+	free(results);
+	return price;
+}

src/gbm_mc.h

@@ -0,0 +1,8 @@
+#ifndef GBM_MC
+#define GBM_MC
+
+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);
+
+#endif

src/optpricer.c

@@ -0,0 +1,78 @@
+#define _XOPEN_SOURCE
+
+#include "black_scholes.h"
+#include "gbm_mc.h"
+
+#include <stdio.h>
+#include <string.h>
+#include <time.h>
+
+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];
+	int opt, type = 0;
+	struct tm expiry, value;
+
+	memset(&expiry, 0, sizeof(expiry));
+	memset(&value, 0, sizeof(value));
+
+	while ((opt = getopt(argc, argv, "s:k:r:v:d:e:n:cp")) != -1) {
+		switch (opt) {
+		case 's':
+			if (sscanf(optarg, "%lf", &spot) == EOF) {
+				return 1;
+			};
+			break;
+		case 'k':
+			if (sscanf(optarg, "%lf", &strike) == EOF) {
+				return 1;
+			};
+			break;
+		case 'r':
+			if (sscanf(optarg, "%lf.", &rfr) == EOF) {
+				return 1;
+			};
+			break;
+		case 'v':
+			if (sscanf(optarg, "%lf", &vol) == EOF) {
+				return 1;
+			};
+			break;
+		case 'n':
+			if (sscanf(optarg, "%lf", &sims) == EOF) {
+				return 1;
+			};
+			break;
+		case 'e':
+			strptime(optarg, "%Y-%m-%d", &expiry);
+			break;
+		case 'd':
+			strptime(optarg, "%Y-%m-%d", &value);
+			break;
+		case 'c':
+			type = 1;
+			break;
+		case 'p':
+			type = -1;
+			break;
+		}
+	}
+
+	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);
+	printf("%s", buffer);
+	return 0;
+}