def test_black_shole_3(self):
N = 16
L = 10
S0 = 100
t = 0.1
r = 0.1
q = 0
sigma = 0.25
strike = 120
c1, c2, c4 = cumulants_from_mgf(general_log_moneyness_mgf,
strike,
BlackScholes(sigma).set_type('mgf'),
t=t,
r=r,
q=q,
S0=S0)
intv_a, intv_b = interval_a_and_b(c1, c2, c4, L)
print(intv_a, intv_b)
exp_res = 0.044
res = cosin_vanilla_call(N, strike, intv_a, intv_b, t, r, q, S0,
BlackScholes(sigma).set_type('chf'))
self.assertAlmostEqual(exp_res, res, 3)
N = 64
res = cosin_vanilla_call(N, strike, intv_a, intv_b, t, r, q, S0,
BlackScholes(sigma).set_type('chf'))
exp_res = 0.045
self.assertAlmostEqual(exp_res, res, 3)
def test_carr_madan_fft_call_pricer_black_shole(self):
N = 2 ** 15
d_u = 0.01
alpha = 1
S0 = 100
t = 1
r = 0.05
q = 0
sigma = 0.3
strike, call_prices = carr_madan_fft_call_pricer(N, d_u, alpha, r, t, S0, q, BlackScholes(sigma).set_type('chf'))
ffn_pricer = spline_fitting(strike, call_prices, 2)
exp_res = 19.6974
res = ffn_pricer(90)
self.assertAlmostEqual(exp_res, res, 4)
def test_cal_price_cosine(self):
cosine_pricer = FourierPricer(self.vanilla_option)
strike_arr = np.array([5, 10, 30, 36, 50, 60, 100])
put_call_arr = np.array(['call', 'call', 'put', 'call', 'call', 'put', 'call'])
exp = np.array([3.09958567e+01, 2.60163625e+01, 8.25753140e-05, 8.12953226e-01,
8.97449491e-11, 2.37785797e+01, 2.19293560e-85, ]
)
volatility = 0.20
N = 150
cosine_pricer.set_log_st_process(BlackScholes(volatility))
cosine_pricer.set_pricing_engine(CosineEngine(N, L=30))
res = cosine_pricer.calc_price(strike_arr, put_call_arr, put_label='put')
npt.assert_array_almost_equal(res, exp, 6)
def test_cal_price_fractional_fft(self):
fft_pricer = FourierPricer(self.vanilla_option)
strike_arr = np.array([5, 10, 30, 36, 50, 60, 100])
put_call_arr = np.array(['call', 'call', 'put', 'call', 'call', 'put', 'call'])
exp = np.array(
[3.09958567e+01, 2.60163625e+01, 8.25753140e-05, 8.12953226e-01,
8.97449491e-11, 2.37785797e+01, 2.19293560e-85, ]
)
volatility = 0.20
N = 2 ** 14
d_u = 0.01
d_k = 0.01
alpha = 1
fft_pricer.set_log_st_process(BlackScholes(volatility))
fft_pricer.set_pricing_engine(FractionFFTEngine(N, d_u, d_k, alpha, spline_order=3))
res = fft_pricer.calc_price(strike_arr, put_call_arr, put_label='put')
npt.assert_array_almost_equal(res, exp, 6)