python_code/Heston Calibration_Vol Surface at master · alebellotta/python_code · GitHub

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import QuantLib as ql
import math

day_count = ql.Actual365Fixed()
calendar = ql.UnitedStates()

calculation_date = ql.Date(6, 11, 2015)

spot = 659.37
ql.Settings.instance().evaluationDate = calculation_date

dividend_yield = ql.QuoteHandle(ql.SimpleQuote(0.0))
risk_free_rate = 0.01
dividend_rate = 0.0
flat_ts = ql.YieldTermStructureHandle(
    ql.FlatForward(calculation_date, risk_free_rate, day_count))
dividend_ts = ql.YieldTermStructureHandle(
    ql.FlatForward(calculation_date, dividend_rate, day_count))

expiration_dates = [ql.Date(6,12,2015), ql.Date(6,1,2016), ql.Date(6,2,2016),
                    ql.Date(6,3,2016), ql.Date(6,4,2016), ql.Date(6,5,2016),
                    ql.Date(6,6,2016), ql.Date(6,7,2016), ql.Date(6,8,2016),
                    ql.Date(6,9,2016), ql.Date(6,10,2016), ql.Date(6,11,2016),
                    ql.Date(6,12,2016), ql.Date(6,1,2017), ql.Date(6,2,2017),
                    ql.Date(6,3,2017), ql.Date(6,4,2017), ql.Date(6,5,2017),
                    ql.Date(6,6,2017), ql.Date(6,7,2017), ql.Date(6,8,2017),
                    ql.Date(6,9,2017), ql.Date(6,10,2017), ql.Date(6,11,2017)]
strikes = [527.50, 560.46, 593.43, 626.40, 659.37, 692.34, 725.31, 758.28]
data = [
[0.37819, 0.34177, 0.30394, 0.27832, 0.26453, 0.25916, 0.25941, 0.26127],
[0.3445, 0.31769, 0.2933, 0.27614, 0.26575, 0.25729, 0.25228, 0.25202],
[0.37419, 0.35372, 0.33729, 0.32492, 0.31601, 0.30883, 0.30036, 0.29568],
[0.37498, 0.35847, 0.34475, 0.33399, 0.32715, 0.31943, 0.31098, 0.30506],
[0.35941, 0.34516, 0.33296, 0.32275, 0.31867, 0.30969, 0.30239, 0.29631],
[0.35521, 0.34242, 0.33154, 0.3219, 0.31948, 0.31096, 0.30424, 0.2984],
[0.35442, 0.34267, 0.33288, 0.32374, 0.32245, 0.31474, 0.30838, 0.30283],
[0.35384, 0.34286, 0.33386, 0.32507, 0.3246, 0.31745, 0.31135, 0.306],
[0.35338, 0.343, 0.33464, 0.32614, 0.3263, 0.31961, 0.31371, 0.30852],
[0.35301, 0.34312, 0.33526, 0.32698, 0.32766, 0.32132, 0.31558, 0.31052],
[0.35272, 0.34322, 0.33574, 0.32765, 0.32873, 0.32267, 0.31705, 0.31209],
[0.35246, 0.3433, 0.33617, 0.32822, 0.32965, 0.32383, 0.31831, 0.31344],
[0.35226, 0.34336, 0.33651, 0.32869, 0.3304, 0.32477, 0.31934, 0.31453],
[0.35207, 0.34342, 0.33681, 0.32911, 0.33106, 0.32561, 0.32025, 0.3155],
[0.35171, 0.34327, 0.33679, 0.32931, 0.3319, 0.32665, 0.32139, 0.31675],
[0.35128, 0.343, 0.33658, 0.32937, 0.33276, 0.32769, 0.32255, 0.31802],
[0.35086, 0.34274, 0.33637, 0.32943, 0.3336, 0.32872, 0.32368, 0.31927],
[0.35049, 0.34252, 0.33618, 0.32948, 0.33432, 0.32959, 0.32465, 0.32034],
[0.35016, 0.34231, 0.33602, 0.32953, 0.33498, 0.3304, 0.32554, 0.32132],
[0.34986, 0.34213, 0.33587, 0.32957, 0.33556, 0.3311, 0.32631, 0.32217],
[0.34959, 0.34196, 0.33573, 0.32961, 0.3361, 0.33176, 0.32704, 0.32296],
[0.34934, 0.34181, 0.33561, 0.32964, 0.33658, 0.33235, 0.32769, 0.32368],
[0.34912, 0.34167, 0.3355, 0.32967, 0.33701, 0.33288, 0.32827, 0.32432],
[0.34891, 0.34154, 0.33539, 0.3297, 0.33742, 0.33337, 0.32881, 0.32492]]

implied_vols[i][j] = data[j][i]
implied_vols = ql.Matrix(len(strikes), len(expiration_dates))
for i in range(implied_vols.rows()):
    for j in range(implied_vols.columns()):
        implied_vols[i][j] = data[j][i]

black_var_surface = ql.BlackVarianceSurface(
    calculation_date, calendar,
    expiration_dates, strikes,
    implied_vols, day_count)

strike = 600.0
expiry = 1.2 # years
black_var_surface.blackVol(expiry, strike)

#### VISUALIZATION

import numpy as np
% matplotlib inline
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm

strikes_grid = np.arange(strikes[0], strikes[-1],10)
expiry = 1.0 # years
implied_vols = [black_var_surface.blackVol(expiry, s)
                for s in strikes_grid] # can interpolate here
actual_data = data[11] # cherry picked the data for given expiry

fig, ax = plt.subplots()
ax.plot(strikes_grid, implied_vols, label="Black Surface")
ax.plot(strikes, actual_data, "o", label="Actual")
ax.set_xlabel("Strikes", size=12)
ax.set_ylabel("Vols", size=12)
legend = ax.legend(loc="upper right")

plot_years = np.arange(0, 2, 0.1)
plot_strikes = np.arange(535, 750, 1)
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y = np.meshgrid(plot_strikes, plot_years)
Z = np.array([black_var_surface.blackVol(y, x)
              for xr, yr in zip(X, Y)
                  for x, y in zip(xr,yr) ]
             ).reshape(len(X), len(X[0]))

surf = ax.plot_surface(X,Y,Z, rstride=1, cstride=1, cmap=cm.coolwarm,
                linewidth=0.1)
fig.colorbar(surf, shrink=0.5, aspect=5)


local_vol_surface = ql.LocalVolSurface(
    ql.BlackVolTermStructureHandle(black_var_surface),
    flat_ts,
    dividend_ts,
    spot)

plot_years = np.arange(0, 2, 0.1)
plot_strikes = np.arange(535, 750, 1)
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y = np.meshgrid(plot_strikes, plot_years)
Z = np.array([local_vol_surface.localVol(y, x)
              for xr, yr in zip(X, Y)
                  for x, y in zip(xr,yr) ]
             ).reshape(len(X), len(X[0]))

surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
                linewidth=0.1)
fig.colorbar(surf, shrink=0.5, aspect=5)


black_var_surface.setInterpolation("bicubic")
local_vol_surface = ql.LocalVolSurface(
    ql.BlackVolTermStructureHandle(black_var_surface),
    flat_ts,
    dividend_ts,
    spot)
plot_years = np.arange(0, 2, 0.15)
plot_strikes = np.arange(535, 750, 10)
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y = np.meshgrid(plot_strikes, plot_years)
Z = np.array([local_vol_surface.localVol(y, x)
              for xr, yr in zip(X, Y)
                  for x, y in zip(xr,yr) ]
             ).reshape(len(X), len(X[0]))

surf = ax.plot_surface(Y,X, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
                linewidth=0.1)
fig.colorbar(surf, shrink=0.5, aspect=5)


#### HESTON CALIBRATION

# dummy parameters
v0 = 0.01; kappa = 0.2; theta = 0.02; rho = -0.75; sigma = 0.5;

process = ql.HestonProcess(flat_ts, dividend_ts,
                           ql.QuoteHandle(ql.SimpleQuote(spot)),
                           v0, kappa, theta, sigma, rho)
model = ql.HestonModel(process)
engine = ql.AnalyticHestonEngine(model)
# engine = ql.FdHestonVanillaEngine(model)

heston_helpers = []
black_var_surface.setInterpolation("bicubic")
one_year_idx = 11 # 12th row in data is for 1 year expiry
date = expiration_dates[one_year_idx]
for j, s in enumerate(strikes):
    t = (date - calculation_date )
    p = ql.Period(t, ql.Days)
    sigma = data[one_year_idx][j]
    #sigma = black_var_surface.blackVol(t/365.25, s)
    helper = ql.HestonModelHelper(p, calendar, spot, s,
                                  ql.QuoteHandle(ql.SimpleQuote(sigma)),
                                  flat_ts,
                                  dividend_ts)
    helper.setPricingEngine(engine)
    heston_helpers.append(helper)


lm = ql.LevenbergMarquardt(1e-8, 1e-8, 1e-8)
model.calibrate(heston_helpers, lm,
                 ql.EndCriteria(500, 50, 1.0e-8,1.0e-8, 1.0e-8))
theta, kappa, sigma, rho, v0 = model.params()

print "theta = %f, kappa = %f, sigma = %f, rho = %f, v0 = %f" % (theta, kappa, sigma, rho, v0)

avg = 0.0

print "%15s %15s %15s %20s" % (
    "Strikes", "Market Value",
     "Model Value", "Relative Error (%)")
print "="*70
for i, opt in enumerate(heston_helpers):
    err = (opt.modelValue()/opt.marketValue() - 1.0)
    print "%15.2f %14.5f %15.5f %20.7f " % (
        strikes[i], opt.marketValue(),
        opt.modelValue(),
        100.0*(opt.modelValue()/opt.marketValue() - 1.0))
    avg += abs(err)
avg = avg*100.0/len(heston_helpers)
print "-"*70
print "Average Abs Error (%%) : %5.3f" % (avg)