def test_price_importance_sampling(self):
strike = 80
asset_num = 1
init_price_vec = 50 * np.ones(asset_num)
vol_vec = 0.2 * np.ones(asset_num)
ir = 0.03
dividend_vec = np.zeros(asset_num)
corr_mat = np.eye(asset_num)
time_to_maturity = 1
random_walk = GBM(time_to_maturity, 100, init_price_vec, ir, vol_vec,
dividend_vec, corr_mat)
analytical2 = Analytical_Sol(init_price_vec[0],
strike,
time_to_maturity,
ir,
vol_vec[0],
dividend_yield=0)
def test_payoff(*l):
return max(np.sum(l) - strike, 0)
test_payoff.strike = strike
opt2 = Euro(test_payoff, random_walk)
real_call, _ = analytical2.european_option_price()
np.random.seed(1)
approx_call = opt2.price_importance_sampling(10000)
np.random.seed(1)
weak_approx_call = opt2.priceV2(10000)
assert abs(approx_call - 0.06082838151186516) < 0.00000000000001
assert abs(approx_call - real_call) / real_call < 0.00297664353761824
assert abs(weak_approx_call -
real_call) / real_call < 0.1362349660567213
def test_price1d_control_variates(self):
strike = 45
asset_num = 1
init_price_vec = 50 * np.ones(asset_num)
vol_vec = 0.3 * np.ones(asset_num)
ir = 0.05
dividend_vec = np.zeros(asset_num)
corr_mat = np.eye(asset_num)
time_to_maturity = 0.25
random_walk = GBM(time_to_maturity, 100, init_price_vec, ir, vol_vec,
dividend_vec, corr_mat)
analytical2 = Analytical_Sol(init_price_vec[0],
strike,
time_to_maturity,
ir,
vol_vec[0],
dividend_yield=0)
def test_payoff(*l):
return max(np.sum(l) - strike, 0)
opt2 = Euro(test_payoff, random_walk)
real_call, _ = analytical2.european_option_price()
np.random.seed(1)
approx_call = opt2.price1d_control_variates(1000)
np.random.seed(1)
approx_call2 = opt2.price(1000)
assert abs(approx_call - 6.412754547048265) < 0.00000000000001
assert abs(approx_call - real_call) / real_call < 0.0025422
assert abs(abs(approx_call2 - real_call) / real_call) < 0.04899
def setUp(self):
strike = 100
asset_num = 1
init_price_vec = 100 * np.ones(asset_num)
vol_vec = 0.1 * np.ones(asset_num)
ir = 0.03
dividend_vec = np.zeros(asset_num)
corr_mat = np.eye(asset_num)
random_walk = GBM(1, 400, init_price_vec, ir, vol_vec, dividend_vec,
corr_mat)
def test_payoff(*l):
return max(strike - np.sum(l), 0)
self.opt1 = Euro(test_payoff, random_walk)
spot_price = init_price_vec[0]
time_to_maturity = 1
interest_rate = 0.03
sigma = 0.1
self.analytical1 = Analytical_Sol(spot_price,
strike,
time_to_maturity,
interest_rate,
sigma,
dividend_yield=0)
def test_Euro1d(self):
T = 1
domain = Domain1d(0, 6, T)
vol, ir, dividend, strike = 0.1, 0.03, 0.01, 1
solver = Euro1d(domain, vol, ir, dividend, strike, CallPutType.PUT)
spot = 1
solver.solve(400, 200)
approx_put = solver.evaluate(spot, T)
analytical = Analytical_Sol(spot, strike, T, ir, vol, dividend_yield=dividend)
_, real_put = analytical.european_option_price()
assert abs(approx_put-0.030050214069580493) < 0.00000000000001
assert abs(approx_put-real_put)/real_put < 0.00054
def restore_helper1d(self, t, nS, model_name, a, b, T, vol, ir, dividend,
strike, cpType):
domain = Domain1d(a, b, T)
solver = Euro1d(domain, vol, ir, dividend, strike, cpType)
Sanaly, S = np.linspace(domain.a, domain.b,
nS), np.linspace(domain.a, domain.b,
nS).reshape(-1, 1)
fitted = solver.restore(S, t * np.ones_like(S), model_name)
real_call, real_put = Analytical_Sol(
Sanaly, strike, T - t, ir, vol,
dividend_yield=dividend).european_option_price()
if cpType == CallPutType.PUT:
real = real_put
elif cpType == CallPutType.CALL:
real = real_call
diff = abs(fitted - real)
plt.plot(Sanaly, real, alpha=0.7, label="Real")
plt.plot(Sanaly, fitted[0], alpha=0.7, label="Approx")
print("error: {}; max error:{}; mean error: {}".format(
diff, np.max(diff), np.mean(diff)))
plt.legend()
plt.show()