import time
# European option price
k_s = np.array([70, 80.0, 90.0, 100.0, 110.0, 120.0, 130.0])
f0 = 100
x0 = np.log(f0)
T = 1
# VG parameters
r = 0.1
sigma = 0.18
theta = -0.13
beta = 0.25
# Upper and lower bound for cos integral
a = -8 * np.sqrt(T)
b = 8 * np.sqrt(T)
cf_VG = partial(JumpDiffusionCharesticFunction.get_VG_cf,
t=T,
x=x0,
r=r,
sigma=sigma,
beta=beta,
theta=theta)
start_time = time.time()
cos_price = np.exp(-r * T) * COSRepresentation.get_european_option_price(
TypeEuropeanOption.CALL, a, b, 2**14, k_s, cf_VG)
end_time = time.time()
diff_time = end_time - start_time
# Upper and lower bound for cos integral
a = -10.0
b = 10.0
# maturities
T = [0.2, 0.4, 0.6, 1.0]
markers = ['.', '+', '*', '^']
no_maturities = len(T)
for i in range(0, no_maturities):
cf_merton = partial(JumpDiffusionCharesticFunction.get_merton_cf, t=T[i], x=x0, sigma=sigma, jumpmean=jumpmean,
jumpstd=jumpstd, lambda_t=lambda_t)
# check martingale
aux = cf_merton(np.asfortranarray(3.0))
cos_price_merton = COSRepresentation.get_european_option_price(TypeEuropeanOption.CALL, a, b, 256, k_s, cf_merton)
iv_smile_merton = []
for k in range(0, no_strikes):
iv_smile_merton.append(implied_volatility(cos_price_merton[k], f0, f0, T[i], 0.0, 0.0, 'c'))
plt.plot(k_s, iv_smile_merton, label='T=%s' % T[i], linestyle='--', color='black', marker=markers[i])
# plt.ylim([0.0, 1.0])
plt.xlabel('K')
plt.legend()
plt.show()
cf_bates = partial(JumpDiffusionCharesticFunction.get_bates_cf,
t=T,
r_t=r,
x=x0,
v=v0,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
jump_mean=muJ,
jump_std=sigmaJ,
jump_intensity=lambdaJ,
b=b2,
u=u2)
start_time = time.time()
cos_price = COSRepresentation.get_european_option_price(
TypeEuropeanOption.CALL, a, b, 256, k_s, cf_bates)
end_time = time.time()
diff_time = end_time - start_time
print(diff_time)
start_time = time.time()
price_cf_integration = []
for i in range(0, no_strikes):
european_option = EuropeanOption(k_s[i], 1.0, TypeSellBuy.BUY,
TypeEuropeanOption.CALL, f0, T)
price_cf_integration.append(
european_option.get_analytic_value(
r,
theta,
rho,
k,
no_maturities = len(T)
for i in range(0, no_maturities):
cf_heston = partial(HestonCharesticFunction.get_trap_cf,
t=T[i],
r_t=0.0,
x=x0,
v=v0,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2)
cos_price_heston = COSRepresentation.get_european_option_price(
TypeEuropeanOption.CALL, a, b, 128, k_s, cf_heston)
iv_smile_heston = []
for j in range(0, no_strikes):
iv_smile_heston.append(
implied_volatility(cos_price_heston[j], f0, f0, T[i], 0.0, 0.0,
'c'))
plt.plot(k_s,
iv_smile_heston,
label='T=%s' % T[i],
linestyle='--',
color='black',
marker=markers[i])
plt.ylim([0.0, 2.0])