SSVI Calibration: Divide by Zero Error

[armarion]

I'm attempting to fit an SSVI surface to equity vols following the example in the notebook below, but using SSVI. When I try to fit SSVI though it produces a division by zero error. Am I doing something wrong?

https://github.com/domokane/FinancePy/blob/master/notebooks/market/volatility/EquityVolSurfaceConstructionSVI.ipynb

Full code and traceback

`import numpy as np
import matplotlib.pyplot as plt
from financepy.market.curves.FinDiscountCurveFlat import FinDiscountCurveFlat
from financepy.market.volatility.FinEquityVolSurface import FinEquityVolSurface
from financepy.finutils.FinDate import FinDate
from financepy.models.FinModelVolatilityFns import FinVolFunctionTypes
valueDate = FinDate(11, 1, 2021)
stockPrice = 3800.0 # Check
expiryDates = [FinDate(11, 2, 2021), FinDate(11, 3, 2021), FinDate(11, 4, 2021),
FinDate(11, 7, 2021), FinDate(11,10, 2021), FinDate(11, 1, 2022),
FinDate(11, 1, 2023)]
strikes = np.array([3037, 3418, 3608, 3703, 3798, 3893, 3988, 4178, 4557], dtype=float)
volSurface = [[42.94, 31.30, 25.88, 22.94, 19.72, 16.90, 15.31, 17.54, 25.67],
[37.01, 28.25, 24.19, 21.93, 19.57, 17.45, 15.89, 15.34, 21.15],
[34.68, 27.38, 23.82, 21.85, 19.83, 17.98, 16.52, 15.31, 18.94],
[31.41, 26.25, 23.51, 22.05, 20.61, 19.25, 18.03, 16.01, 15.90],
[29.91, 25.58, 23.21, 22.01, 20.83, 19.70, 18.62, 16.63, 14.94],
[29.26, 25.24, 23.03, 21.91, 20.81, 19.73, 18.69, 16.76, 14.63],
[27.59, 24.33, 22.72, 21.93, 21.17, 20.43, 19.71, 18.36, 16.26]]
volSurface = np.array(volSurface)
volSurface = volSurface / 100.0
rfrRate = 0.020 # USD
discountCurve = FinDiscountCurveFlat(valueDate, rfrRate)
divRate = 0.010 # USD
dividendCurve = FinDiscountCurveFlat(valueDate, divRate)
volFunctionType = FinVolFunctionTypes.SSVI
equitySurface = FinEquityVolSurface(valueDate, stockPrice, discountCurve,dividendCurve, expiryDates,strikes,volSurface, volFunctionType)
tol = 1e-4
equitySurface.checkCalibration(False, tol)

Failed to converge, will try CG
Traceback (most recent call last):
File "C:\Users\armar\anaconda3\lib\site-packages\financepy\market\volatility\FinEquityVolSurface.py", line 116, in _solveToHorizon
opt = minimize(_obj, xinits, args, method="Nelder-Mead", tol=tol)
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_minimize.py", line 606, in minimize
return _minimize_neldermead(fun, x0, args, callback, **options)
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize\optimize.py", line 689, in _minimize_neldermead
fsim[k] = func(sim[k])
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize\optimize.py", line 427, in function_wrapper
return function(*(wrapper_args + args))
ZeroDivisionError: division by zero
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "C:\Users\armar\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3418, in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
File "", line 39, in
equitySurface = FinEquityVolSurface(valueDate,
File "C:\Users\armar\anaconda3\lib\site-packages\financepy\market\volatility\FinEquityVolSurface.py", line 277, in init
self._buildVolSurface(finSolverType=finSolverType)
File "C:\Users\armar\anaconda3\lib\site-packages\financepy\market\volatility\FinEquityVolSurface.py", line 638, in _buildVolSurface
res = _solveToHorizon(s, t, r, q,
File "C:\Users\armar\anaconda3\lib\site-packages\financepy\market\volatility\FinEquityVolSurface.py", line 125, in _solveToHorizon
opt = minimize(_obj, xinits, args, method="CG", tol=tol)
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_minimize.py", line 610, in minimize
return _minimize_cg(fun, x0, args, jac, callback, **options)
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize\optimize.py", line 1423, in _minimize_cg
sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps,
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize\optimize.py", line 261, in _prepare_scalar_function
sf = ScalarFunction(fun, x0, args, grad, hess,
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_differentiable_functions.py", line 76, in init
self._update_fun()
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_differentiable_functions.py", line 166, in _update_fun
self._update_fun_impl()
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_differentiable_functions.py", line 73, in update_fun
self.f = fun_wrapped(self.x)
File "C:\Users\armar\anaconda3\lib\site-packages\scipy\optimize_differentiable_functions.py", line 70, in fun_wrapped
return fun(x, *args)
ZeroDivisionError: division by zero
`

[domokane]

There is an issue with the starting parameters for the calibration. I will look at this as soon as I get time. It may be a while. Unless you would like to investigate it.

[abhi-g80]

I am not getting division by zero error but the fit doesn't seem to good. Example,

[domokane]

This needs further work. I will look at it as soon as I can.