def test_conv_rate_5dDig(self):
dim = 6
T = 1
strike = 40
init_price_vec = np.full(dim, 40)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
euro = Digital(strike, init_price_vec, T, ir, vol, dividend, corr, 1)
result = FFTConvExperiment(0.45, 2, 7, euro, 10, True)
hdpPickle.dump(result, 'FFTconv_rate_5dDig.pickle')
print(result)
def test_conv_rate_6dBas(self):
dim = 6
T = 1
strike = 40
init_price_vec = np.full(dim, 40)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
euro = BasEuro(strike, init_price_vec, T, ir, vol, dividend, corr, -1)
result = FFTConvExperiment(1.50600, 2, 6, euro, 10, True)
hdpPickle.dump(result, 'FFTconv_rate_6dBas.pickle')
print(result)
def test_delta_4d(self):
dim = 4
T = 1
strike = 40
init_price_vec = np.full(4, 40, dtype=np.float64)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
euro = GAEuro(strike, init_price_vec, T, ir, vol, dividend, corr, 1)
analy = AnalyticalGA(dim, init_price_vec, strike, T, ir, vol, dividend,
corr).delta()
result = FFTConvDeltaExperiment(analy[0], 3, 8, euro, 10)
hdpPickle.dump(result, 'FFTconv_delta_4dGA.pickle')
print(result)
def test_conv_rate_4dGA(self):
dim = 4
T = 1
strike = 40
init_price_vec = np.full(4, 40, dtype=np.float64)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
euro = GAEuro(strike, init_price_vec, T, ir, vol, dividend, corr, 1)
analy = AnalyticalGA(dim, init_price_vec, strike, T, ir, vol, dividend,
corr).european_option_price()
result = FFTConvExperiment(analy, 3, 7, euro, 10)
hdpPickle.dump(result, 'FFTconv_rate_4dGA.pickle')
print(result)
def test_plot_loss(self):
loss_vec = pickle.load("BlackScholes_AmericanPut1217_lossvec.pickle")
l1_vec = pickle.load("BlackScholes_AmericanPut1217_l1vec.pickle")
l2_vec = pickle.load("BlackScholes_AmericanPut1217_l2vec.pickle")
l3_vec = pickle.load("BlackScholes_AmericanPut1217_l3vec.pickle")
l4_vec = pickle.load("BlackScholes_AmericanPut1217_l4vec.pickle")
domain = np.arange(1, 3001)
all_vec = [domain, loss_vec, l1_vec, l2_vec, l3_vec, l4_vec]
for i in range(len(all_vec)):
all_vec[i] = all_vec[i][::50]
plt.plot(all_vec[0], all_vec[1], linewidth=2)
for i in range(2, len(all_vec)):
plt.plot(all_vec[0], all_vec[i], '--')
plt.legend(['Sum', 'L1', 'L2', 'L3', 'L4'])
plt.xlabel('Iterations')
plt.ylabel('Loss')
# plt.plot(domain, loss_vec, domain, l1_vec, domain, l2_vec, domain, l3_vec, domain, l4_vec)
plt.yscale('log')
plt.savefig("loss.png", dpi=1000)
def test_amer(self):
# although this is not a euro experiment...
T = 1
strike = 50
asset_num = 1
init_price_vec = 50*np.ones(asset_num)
vol_vec = 0.5*np.ones(asset_num)
ir = 0.05
dividend_vec = np.zeros(asset_num)
corr_mat = np.eye(asset_num)
nTime = 365
random_walk = GBM(T, nTime, init_price_vec, ir, vol_vec, dividend_vec, corr_mat)
def test_payoff(*l):
return max(strike - np.sum(l), 0)
opt = American(test_payoff, random_walk)
analy = 8.723336355455928
np.random.seed(1)
result = MCEuroExperiment(analy, 10, 16, opt, "V1")
hdpPickle.dump(result, 'MCAmer_1d.pickle')
print(result)
def test_conv_rate_6d_control_sobol(self):
dim = 6
T = 1
strike = 40
init_price_vec = np.full(dim, 40)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
vol_vec = np.full(dim, vol)
dividend_vec = np.full(dim, dividend)
corr_mat = np.full((dim, dim), corr)
np.fill_diagonal(corr_mat, 1)
payoff_func = lambda x: np.maximum(strike - np.mean(x, axis=1), np.zeros(len(x)))
random_walk = GBM(T, 400, init_price_vec, ir, vol_vec, dividend_vec, corr_mat)
opt = Euro(payoff_func, random_walk)
analy = 1.50600
np.random.seed(1)
result = MCEuroExperiment(analy, 14, 21, opt, "V8")
hdpPickle.dump(result, 'MCEuro_6d_control_sobol.pickle')
print(result)
def test_conv_rate_4dGA_anti_sol(self):
from scipy.stats.mstats import gmean
dim = 4
T = 1
strike = 40
init_price_vec = np.full(dim, 40)
vol = 0.2
ir = 0.06
dividend = 0.04
corr = 0.25
vol_vec = np.full(dim, vol)
dividend_vec = np.full(dim, dividend)
corr_mat = np.full((dim, dim), corr)
np.fill_diagonal(corr_mat, 1)
payoff_func = lambda x: np.maximum((gmean(x, axis=1) - strike), np.zeros(len(x)))
random_walk = GBM(T, 400, init_price_vec, ir, vol_vec, dividend_vec, corr_mat)
opt = Euro(payoff_func, random_walk)
analy = 2.165238512096621
np.random.seed(1)
result = MCEuroExperiment(analy, 20, 24, opt, "V6")
hdpPickle.dump(result, 'MCEuro_4dGA_AntiSol.pickle')
print(result)
def run(self, n_samples, steps_per_sample, n_layers=3, layer_width=50, n_interior=32,\
n_terminal=32, saved_name=None, use_fd_hessian=False, use_L2_err=True):
if not saved_name:
pickle_dir = DIR_LOC + "/saved_models/{}_Euro".format(
time.strftime("%Y%m%d"))
saved_name = "{}_Euro.ckpt".format(time.strftime("%Y%m%d"))
else:
pickle_dir = DIR_LOC + "/saved_models/{}_{}".format(
time.strftime("%Y%m%d"), saved_name)
saved_name = time.strftime("%Y%m%d") + "_" + saved_name + ".ckpt"
model = DGMNet(n_layers, layer_width, input_dim=self.dim)
self.model = model
S_interior_tnsr = tf.placeholder(tf.float64, [None, self.dim])
t_interior_tnsr = tf.placeholder(tf.float64, [None, 1])
S_terminal_tnsr = tf.placeholder(tf.float64, [None, self.dim])
t_terminal_tnsr = tf.placeholder(tf.float64, [None, 1])
L1_tnsr, L3_tnsr = self.loss_func(model, S_interior_tnsr, t_interior_tnsr,\
S_terminal_tnsr, t_terminal_tnsr, use_fd_hessian=use_fd_hessian, use_L2_err=use_L2_err)
loss_tnsr = L1_tnsr + L3_tnsr
global_step = tf.Variable(0, trainable=False)
boundaries = [5000, 10000, 20000, 30000, 40000, 45000]
values = [1e-4, 5e-5, 1e-5, 5e-6, 1e-6, 5e-7, 1e-7]
learning_rate = tf.train.piecewise_constant(global_step, boundaries,
values)
optimizer = tf.train.AdamOptimizer(
learning_rate=learning_rate).minimize(loss_tnsr)
model_saver = tf.train.Saver()
self.loss_vec, self.L1_vec, self.L3_vec = [], [], []
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
for i in range(n_samples):
S_interior, t_interior, S_terminal, t_terminal = self.sampler.run(
n_interior, n_terminal)
for _ in range(steps_per_sample):
loss, L1, L3, _ = sess.run([loss_tnsr, L1_tnsr, L3_tnsr, optimizer],\
feed_dict={S_interior_tnsr: S_interior, t_interior_tnsr: t_interior,\
S_terminal_tnsr: S_terminal, t_terminal_tnsr: t_terminal})
self.loss_vec.append(loss)
self.L1_vec.append(L1)
self.L3_vec.append(L3)
print("Iteration {}: Loss: {}; L1: {}; L3: {}".format(
i, loss, L1, L3))
model_saver.save(sess, DIR_LOC + "/saved_models/" + saved_name)
pickle.dump(self.loss_vec, pickle_dir + "_lossvec.pickle")
pickle.dump(self.L1_vec, pickle_dir + "_l1vec.pickle")
# pickle.dump(self.L2_vec, pickle_dir+"_l2vec.pickle")
pickle.dump(self.L3_vec, pickle_dir + "_l3vec.pickle")