def test_analytical_vega(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S, K, t, r, sigma = row['S'], row['K'], row['t'], row['R'], row[
'v']
self.assertAlmostEqual(analytical.vega('c', S, K, t, r, sigma, q),
row['CV'] * .01,
delta=0.000001)
self.assertAlmostEqual(analytical.vega('p', S, K, t, r, sigma, q),
row['PV'] * .01,
delta=0.000001)
def test_analytical_vega(self):
S = 49
K = 50
sigma = .2
r = .05
t = 0.3846
q = 0.2
flag = 'p'
c_put = c_analytical.vega(flag, S, K, t, r, sigma, q)
py_put = py_analytical.vega(flag, S, K, t, r, sigma, q)
self.assertTrue(almost_equal(c_put, py_put))
flag = 'c'
c_call = c_analytical.vega(flag, S, K, t, r, sigma, q)
py_call = py_analytical.vega(flag, S, K, t, r, sigma, q)
self.assertTrue(almost_equal(c_call, py_call))
def test_vega(self):
vegas = [
vega(flag, S, K, t, r, sigma, q)
for flag, S, K, t, r, sigma, q in self.arg_combinations
]
nvegas = [
nvega(flag, S, K, t, r, sigma, q)
for flag, S, K, t, r, sigma, q in self.arg_combinations
]
self.assertTrue(self.diff_mean(vegas, nvegas) < self.epsilon)
def get_malliavin_greeks_bs_flat(s0: float, t: float, no_steps: int,
no_paths: int, r: float, q: float,
sigma: float, payoff: Callable[[ndarray],
ndarray],
euler_scheme: EULER_SCHEME_TYPE):
shift_delta = 0.01
shift_vega = 0.01
z = np.random.standard_normal(size=(no_paths, no_steps - 1))
drift_t = partial(bs_drift_flat, rate_t=r, dividend_t=q)
sigma_t = partial(bs_sigma_flat, sigma_t=sigma)
sigma_t_shift = partial(bs_sigma_flat, sigma_t=sigma + shift_vega)
s_t = sde_euler_simulation(0.0, t, s0, no_steps, no_paths, z, drift_t,
sigma_t, euler_scheme)
s_t_shift_delta = sde_euler_simulation(0.0, t, s0 + shift_delta, no_steps,
no_paths, z, drift_t, sigma_t,
euler_scheme)
s_t_shift_vega = sde_euler_simulation(0.0, t, s0, no_steps, no_paths, z,
drift_t, sigma_t_shift, euler_scheme)
phi_t = payoff(s_t[:, -1])
mc_price = np.average(phi_t) * np.exp(-r * t)
mc_price_delta = np.average(payoff(s_t_shift_delta[:, -1])) * np.exp(
-r * t)
mc_price_vega = np.average(payoff(s_t_shift_vega[:, -1])) * np.exp(-r * t)
delta = analytical.delta('c', s0, 90, t, r, sigma, q)
price = black_scholes_merton('c', s0, 90, t, r, sigma, q)
vega = analytical.vega('c', s0, 90, t, r, sigma, q) * 100
mc_delta = (mc_price_delta - mc_price) / shift_delta
malliavin_delta = get_malliavin_delta_bs_flat(phi_t, s_t[:, -1], s0, sigma,
r, q, t)
mc_vega = (mc_price_vega - mc_price) / shift_vega
malliavin_vega = get_malliavin_vega_bs_flat(phi_t, s_t[:, -1], s0, sigma,
r, q, t)
return mc_delta, malliavin_delta
def vega(self, S, vol):
return bsg.vega(self.flag, S, self.K, option.time_exp[self.exp],
self.rate, vol, 0.)