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_heston(self):
N = 100
L = 10
S0 = 100
t = 0.5
k = 2
r = 0.03
q = 0
sigma = 0.5
theta = 0.04
V0 = 0.04
rho = -0.7
strike = 90
c1, c2, c4 = cumulants_from_mgf(general_log_moneyness_mgf,
strike,
Heston(V0, theta, k, sigma,
rho).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 = 13.2023
res = cosin_vanilla_call(
N, strike, intv_a, intv_b, t, r, q, S0,
Heston(V0, theta, k, sigma, rho).set_type('chf'))
self.assertAlmostEqual(exp_res, res, 3)
def test_vg(self):
N = 150
L = 10
S0 = 100
t = 1 / 12
r = 0.1
q = 0
sigma = 0.12
theta = -0.14
v = 0.2
strike = 90
c1, c2, c4 = cumulants_from_mgf(general_log_moneyness_mgf,
strike,
VarianceGamma(theta, v,
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)
res = cosin_vanilla_call(
N, strike, intv_a, intv_b, t, r, q, S0,
VarianceGamma(theta, v, sigma).set_type('chf'))
exp_res = 10.8289
self.assertAlmostEqual(exp_res, res, 4)
def calc_integral_interval(self, strike, L, t, r, q, S0, chf_ln_st):
c1, c2, c4 = cumulants_from_mgf(general_log_moneyness_mgf,
strike,
chf_ln_st.set_type('mgf'),
t=t,
r=r,
q=q,
S0=S0)
a, b = interval_a_and_b(c1, c2, c4, L)
return a, b