def calibslice(lvol):
lvolf = np.maximum(0, lvol)
interped = intp.interp1d(calibki,
lvolf,
kind=1,
fill_value="extrapolate")
lvolj = interped(R[i - 1])
volj = volji * lvolj
#print(lvol)
R[i] = R[i - 1] * dffor[i - 1] / dfdom[i - 1] * np.exp(
-volj * volj * t / 2 + paths[i - 1] * volj * math.sqrt(t))
driftadj = np.mean(R[i]) / fwd
R[i] = R[i] / driftadj
volsim = [
BS.volfromsim(R[i], fwd, strk, i * t) for strk in calibki
]
#err = np.linalg.norm(np.log(volsim) - np.log(volcalibi))
err = np.linalg.norm(volsim - volcalibi)
#if i == 1 :
# print(err, volsim, volcalibi)
return err
cdf0 = vu.cdf(BS.mccdf(R[i]))
err = np.linalg.norm(
np.log(cdf0.probinterpinv(cumppt)) -
np.log(cdf1.probinterpinv(cumppt)))
print(err)
return err * err
def getstrikevol(self, strikes, mat):
simul = self.getsimulation(500000)
fwd = simul.mean()
print("Fwd", fwd)
fwd = 15.0
strikevol = np.zeros((strikes.shape[0], 2))
strikevol[:, 0] = strikes
strikevol[:, 1] = np.array(
[BS.volfromsim(simul, fwd, stri, mat) for stri in strikes])
return strikevol
def testquadsmile():
fwd = 15.0
T = 10
a = 0.5
b = 0.0001
c = 1.05
stvol = np.ones([1000, 2])
stvol[:, 0] = np.exp(np.linspace(np.log(0.5), np.log(100), 1000))
stvol[:, 1] = 0.2
stvol[:, 1] = 0.2 * du.quad(np.log(stvol[:, 0] / fwd) / 0.2 / T, a, b, c)
vol = logvolslice(stvol, fwd, T)
cdfvol = vol.cumdf.strikeprob
plt.plot(cdfvol[:, 0], cdfvol[:, 1])
plt.title("cdf")
plt.show()
pdfvol = vol.cumdf.getpdf()
plt.plot(pdfvol[:, 0], pdfvol[:, 1])
plt.title("pdf")
plt.show()
strvol = vol.cumdf.getstrikevol(stvol[:, 0], vol.mat)
plt.plot(stvol[:, 0], stvol[:, 1], label="input quadvoL")
plt.plot(strvol[:, 0], strvol[:, 1], label="vol from cdf")
plt.title("vol from cdf")
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.show()
xran = np.random.normal(size=10000)
vols = 0.2
sim = fwd * np.exp(-vols * vols * T / 2 + vols * xran * math.sqrt(T))
lbound = vol.cumdf.getstrike(0.01)
ubound = vol.cumdf.getstrike(0.99)
print(lbound, ubound)
x = np.linspace(ubound, lbound, 30)
y = [BS.volfromsim(sim, sim.mean(), stri, T) for stri in x]
plt.plot(x, y)
plt.title("vol from cdf")
plt.show()
print(vol.deltastrike(0.25, 1), vol.deltastrike(0.25, -1))
print(vol.getrr(0.25), vol.getfly(0.25))
print(vol.deltastrike(0.1, 1), vol.deltastrike(0.1, -1))
print(vol.getrr(0.1), vol.getfly(0.1))
strikevolsmile = fivepointtostrikevol(15, 0.20, -0.06, 0.01, -0.12, 0.03,
5)
plt.plot(strikevolsmile[:, 0], strikevolsmile[:, 1])
plt.title("interpolated smile")
plt.show()
return vol