def fivepointtostrikevol(fwd, atm, rr25, fly25, rr10, fly10, mat):
''' create volslice with atm vol
transform strikes with a quadratic
'''
strikevol = fivepointsmile(fwd, atm, rr25, fly25, rr10, fly10, mat)
strikevolbase = fivepointsmile(fwd, atm, 0, 0, 0, 0, mat)
strikevolmap = interpolate.interp1d(np.log(strikevolbase[:, 0]),
np.log(strikevol[:, 0]),
fill_value="extrapolate",
kind=2)
lbound = BS.blackstrikefordelta(atm, strikevol[0, 0], mat, -1, 0.01)
ubound = BS.blackstrikefordelta(atm, strikevol[-1, 0], mat, 1, 0.01)
stvol = np.ones([1000, 2])
stvol[:, 0] = np.linspace(lbound, ubound, 1000)
stvol[:, 1] = atm
vol = logvolslice(stvol, fwd, mat)
baseprob = vol.cumdf.strikeprob
prob = baseprob.copy()
prob[:,
0] = [np.exp(strikevolmap(np.log(stri))) for stri in baseprob[:, 0]]
prob[:, 1] = baseprob[:, 1]
plt.plot(prob[:, 0], prob[:, 1], label="smile")
plt.plot(baseprob[:, 0], baseprob[:, 1], label="nonsmile")
plt.title("smile")
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.show()
strikevol = cdf(prob).getstrikevol(prob[:, 0], mat)
return strikevol
def fivepointsmile(fwd, atm, rr25, fly25, rr10, fly10, mat):
c25 = 0.5 * (rr25 + 2 * fly25 + 2 * atm)
p25 = c25 - rr25
c10 = 0.5 * (rr10 + 2 * fly10 + 2 * atm)
p10 = c10 - rr10
kc25 = BS.blackstrikefordelta(c25, fwd, mat, 1, 0.25)
kc10 = BS.blackstrikefordelta(c10, fwd, mat, 1, 0.1)
kp25 = BS.blackstrikefordelta(p25, fwd, mat, -1, 0.25)
kp10 = BS.blackstrikefordelta(p10, fwd, mat, -1, 0.1)
strikevol = np.ones((5, 2))
strikevol[0, 0] = kp10
strikevol[0, 1] = p10
strikevol[1, 0] = kp25
strikevol[1, 1] = p25
strikevol[2, 0] = fwd
strikevol[2, 1] = atm
strikevol[3, 0] = kc25
strikevol[3, 1] = c25
strikevol[4, 0] = kc10
strikevol[4, 1] = c10
return strikevol