def Fourier_inversion(self):
"""
Price obtained by inversion of the characteristic function
"""
k = np.log(self.K / self.S0) # log moneyness
w = -np.log(1 - self.theta * self.kappa - self.kappa / 2 *
self.sigma**2) / self.kappa # coefficient w
cf_VG_b = partial(cf_VG,
t=self.T,
mu=(self.r - w),
theta=self.theta,
sigma=self.sigma,
kappa=self.kappa)
right_lim = 5000 # using np.inf may create warnings
if self.payoff == "call":
call = self.S0 * Q1(k, cf_VG_b, right_lim) - self.K * np.exp(
-self.r * self.T) * Q2(k, cf_VG_b,
right_lim) # pricing function
return call
elif self.payoff == "put":
put = self.K * np.exp(-self.r * self.T) * (
1 - Q2(k, cf_VG_b, right_lim)) - self.S0 * (
1 - Q1(k, cf_VG_b, right_lim)) # pricing function
return put
else:
raise ValueError("invalid type. Set 'call' or 'put'")
def Fourier_inversion(self):
"""
Price obtained by inversion of the characteristic function
"""
k = np.log(self.K / self.S0) # log moneyness
m = self.lam * (np.exp(self.muJ +
(self.sigJ**2) / 2) - 1) # coefficient m
cf_Mert = partial(cf_mert,
t=self.T,
mu=(self.r - 0.5 * self.sig**2 - m),
sig=self.sig,
lam=self.lam,
muJ=self.muJ,
sigJ=self.sigJ)
if self.payoff == "call":
call = self.S0 * Q1(k, cf_Mert, np.inf) - self.K * np.exp(
-self.r * self.T) * Q2(k, cf_Mert, np.inf) # pricing function
return call
elif self.payoff == "put":
put = self.K * np.exp(
-self.r * self.T) * (1 - Q2(k, cf_Mert, np.inf)) - self.S0 * (
1 - Q1(k, cf_Mert, np.inf)) # pricing function
return put
else:
raise ValueError("invalid type. Set 'call' or 'put'")
def Fourier_inversion(self):
"""
Price obtained by inversion of the characteristic function
"""
k = np.log(self.K / self.S0) # log moneyness
cf_H_b_good = partial(cf_Heston_good,
t=self.T,
v0=self.v0,
mu=self.r,
theta=self.theta,
sigma=self.sigma,
kappa=self.kappa,
rho=self.rho)
limit_max = 2000 # right limit in the integration
if self.payoff == "call":
call = self.S0 * Q1(k, cf_H_b_good, limit_max) \
- self.K * np.exp(-self.r*self.T) * Q2(k, cf_H_b_good, limit_max)
return call
elif self.payoff == "put":
put = self.K * np.exp(-self.r*self.T) * (1 - Q2(k, cf_H_b_good, limit_max)) \
- self.S0 * (1-Q1(k, cf_H_b_good, limit_max))
return put
else:
raise ValueError("invalid type. Set 'call' or 'put'")
def Fourier_inversion(self):
"""
Price obtained by inversion of the characteristic function
"""
k = np.log(self.K / self.S0)
cf_GBM = partial(cf_normal,
mu=(self.r - 0.5 * self.sig**2) * self.T,
sig=self.sig * np.sqrt(self.T)) # function binding
if self.payoff == "call":
call = self.S0 * Q1(k, cf_GBM, np.inf) - self.K * np.exp(
-self.r * self.T) * Q2(k, cf_GBM, np.inf) # pricing function
return call
elif self.payoff == "put":
put = self.K * np.exp(
-self.r * self.T) * (1 - Q2(k, cf_GBM, np.inf)) - self.S0 * (
1 - Q1(k, cf_GBM, np.inf)) # pricing function
return put
else:
raise ValueError("invalid type. Set 'call' or 'put'")
def Fourier_inversion(self):
"""
Price obtained by inversion of the characteristic function
"""
k = np.log(self.K/self.S0) # log moneyness
w = ( 1 - np.sqrt( 1 - 2*self.theta*self.kappa -self.kappa*self.sigma**2) )/self.kappa # martingale correction
cf_NIG_b = partial(cf_NIG, t=self.T, mu=(self.r-w), theta=self.theta, sigma=self.sigma, kappa=self.kappa )
if self.payoff == "call":
call = self.S0 * Q1(k, cf_NIG_b, np.inf) - self.K * np.exp(-self.r*self.T) * Q2(k, cf_NIG_b, np.inf) # pricing function
return call
elif self.payoff == "put":
put = self.K * np.exp(-self.r*self.T) * (1 - Q2(k, cf_NIG_b, np.inf)) - self.S0 * (1-Q1(k, cf_NIG_b, np.inf)) # pricing function
return put
else:
raise ValueError("invalid type. Set 'call' or 'put'")