def test_heston(self):
"""Test Heston model."""
price, strike = 100, 90
riskfree, maturity = 0, 30 / 365
moneyness = np.log(strike / price) - riskfree * maturity
lm = 1.5768
mu = .12**2
eta = .5751
rho = -.0
sigma = .12**2
param = HestonParam(lm=lm, mu=mu, eta=eta, rho=rho, sigma=sigma)
model = Heston(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
self.assertEqual(premium.shape, (1, ))
moneyness = np.linspace(-.1, .1, 10)
premium = cosmethod(model, moneyness=moneyness, call=True)
self.assertEqual(premium.shape, moneyness.shape)
riskfree = np.zeros_like(moneyness)
premium = cosmethod(model, moneyness=moneyness, call=True)
self.assertEqual(premium.shape, moneyness.shape)
def single_premium():
"""Test COS method for floats.
"""
price, strike = 100, 90
riskfree, maturity = 0, 30 / 365
sigma = .15
moneyness = np.log(strike / price) - riskfree * maturity
model = GBM(GBMParam(sigma=sigma), riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
nu = .2
theta = -.14
sigma = .25
param = VarGammaParam(theta=theta, nu=nu, sigma=sigma)
model = VarGamma(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
lm = 1.5768
mu = .12**2
eta = .5751
rho = -.0
sigma = .12**2
param = HestonParam(lm=lm, mu=mu, eta=eta, rho=rho, sigma=sigma)
model = Heston(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
rho = .55
delta = .75
mu = .2**2 / 365
sigma = .2**2 / 365
phi = -.0
theta1 = -16.0
theta2 = 20.95
param = ARGParam(rho=rho,
delta=delta,
mu=mu,
sigma=sigma,
phi=phi,
theta1=theta1,
theta2=theta2)
model = ARG(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
def cos_heston_price(S_0, K, r, T, v, v_0, kappa, gamma, rho, call=True):
"""
Pricer for European option (single asset) under Heston dynamic
:param S_0: init stock price
:param K: strike
:param r: risk-free rate
:param T: maturity
:param v: long term mean variance
:param v_0: initial variance
:param kappa: reversion speed
:param gamma: vol coefficient of vol
:param rho: correlation between stock and volatility dynamic
:param call: call if True, put otherwise
:return: Option price
"""
moneyness = np.log(K / S_0) - r * T
param = HestonParam(lm=kappa, mu=v, eta=gamma, rho=rho, sigma=v_0)
model = Heston(param, r, T)
P = cosmethod(model, moneyness=moneyness, call=call)
return P[0]
def multiple_premia_heston(nobs=2000):
"""Test COS method on the grid.
"""
lm = 1.5768
mu = .12**2
eta = .5751
rho = -.0
sigma = .12**2
price = 1
strike = np.exp(np.linspace(-.1, .1, nobs))
maturity = 30 / 365
riskfree = .01 * np.ones(nobs)
moneyness = np.log(strike / price) - riskfree * maturity
call = np.ones_like(moneyness).astype(bool)
call[moneyness < 0] = False
param = HestonParam(lm=lm, mu=mu, eta=eta, rho=rho, sigma=sigma)
model = Heston(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=call)
plt.plot(strike, premium)
plt.show()