def CubSpline_DeltaIntrp_Solving(K, X, Y, CPSign, S, VAtm, Rd, Rf, Te, Td,
Premium, DeltaMode):
## Calculate Cubic Spline Function Parameters
a, b, c, d = CubicSplinePara(X, Y, 'Clamped')
Delta = lambda V: OptionDelta(CPSign, S, K, V, Rd, Rf, Te, Td, Premium,
DeltaMode)
VIntrp = lambda V: CubicSplineVol(Delta(V), X, a, b, c, d)
V_Diff = lambda V: VIntrp(V) - V
V_K = opt.newton(V_Diff, VAtm, tol=1e-4)
return V_K, a, b, c, d
def CubSpline_LogMon5P_Flat(X_XIntrp, XQuotes, VQuotes ):
## Calculate Cubic Spline Function Parameters
a,b,c,d = CubicSplinePara(XQuotes, VQuotes, 'Natural')
## Calculate Interpolated Vols
if X_XIntrp >= XQuotes[0]:
V_XIntrp = VQuotes[0]
elif X_XIntrp <= XQuotes[-1]:
V_XIntrp = VQuotes[-1]
else:
V_XIntrp = CubicSplineVol(X_XIntrp, XQuotes, a,b,c,d)
return V_XIntrp
def CubSpline_LogMon9P(X_XIntrp, XQuotes, VQuotes ):
## Calculate Cubic Spline Function Parameters
a,b,c,d = CubicSplinePara(XQuotes, VQuotes, 'Clamped')
## Calculate Interpolated Vols
if X_XIntrp >= XQuotes[0]:
V_XIntrp = LinearExtrapolateVol(X_XIntrp, XQuotes[0], XQuotes[1], VQuotes[0], VQuotes[1])
elif X_XIntrp <= XQuotes[-1]:
V_XIntrp = LinearExtrapolateVol(X_XIntrp, XQuotes[-1], XQuotes[-2], VQuotes[-1], VQuotes[-2])
else:
V_XIntrp = CubicSplineVol(X_XIntrp, XQuotes, a,b,c,d)
return V_XIntrp
def CubSpline_LogMon5P_Flat(X_XIntrp, XQuotes, VQuotes):
## Calculate Cubic Spline Function Parameters
a, b, c, d = CubicSplinePara(XQuotes, VQuotes, 'Natural')
## Initialization
NX = len(XQuotes)
NIntrp = len(X_XIntrp)
V_XIntrp = np.zeros_like(X_XIntrp)
## Calculate Interpolated Vols
for i in range(NIntrp):
if X_XIntrp[i] >= XQuotes[0]:
V_XIntrp[i] = VQuotes[0]
elif X_XIntrp[i] <= XQuotes[-1]:
V_XIntrp[i] = VQuotes[-1]
else:
V_XIntrp[i] = CubicSplineVol(X_XIntrp[i], XQuotes, a, b, c, d)
return V_XIntrp, a, b, c, d
def CubSpline_LinExt_DeltaIntrp(DIntrp, X, Y):
## Calculate Cubic Spline Function Parameters
a, b, c, d = CubicSplinePara(X, Y, 'Clamped')
## Initialization
NX = len(X)
NIntrp = len(DIntrp)
YIntrp = np.zeros_like(DIntrp)
## Calculate Interpolated Vols
for i in range(NIntrp):
if DIntrp[i] >= X[0]:
YIntrp[i] = LinearExtrapolateVol(DIntrp[i], X[0], X[1], Y[0], Y[1])
elif DIntrp[i] <= X[-1]:
YIntrp[i] = LinearExtrapolateVol(DIntrp[i], X[-1], X[-2], Y[-1],
Y[-2])
else:
YIntrp[i] = CubicSplineVol(DIntrp[i], X, a, b, c, d)
return YIntrp, a, b, c, d
def CubSpline_LogMon5P_Linear(X_XIntrp, XQuotes, VQuotes):
## Calculate Cubic Spline Function Parameters
a, b, c, d = CubicSplinePara(XQuotes, VQuotes, 'Clamped')
## Initialization
NX = len(XQuotes)
NIntrp = len(X_XIntrp)
V_XIntrp = np.zeros_like(X_XIntrp)
## Calculate Interpolated Vols
for i in range(NIntrp):
if X_XIntrp[i] >= XQuotes[0]:
V_XIntrp[i] = LinearExtrapolateVol(X_XIntrp[i], XQuotes[0],
XQuotes[1], VQuotes[0],
VQuotes[1])
elif X_XIntrp[i] <= XQuotes[-1]:
V_XIntrp[i] = LinearExtrapolateVol(X_XIntrp[i], XQuotes[-1],
XQuotes[-2], VQuotes[-1],
VQuotes[-2])
else:
V_XIntrp[i] = CubicSplineVol(X_XIntrp[i], XQuotes, a, b, c, d)
return V_XIntrp, a, b, c, d