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# ---
# jupyter:
# jupytext:
# formats: py:percent
# text_representation:
# extension: .py
# format_name: percent
# format_version: '1.3'
# jupytext_version: 1.4.2
# kernelspec:
# display_name: Python 3
# language: python
# name: python3
# ---
# %% [markdown]
# # Leverage function for the Heston SLV model
#
# Copyright (©) 2019 Klaus Spanderen
#
# This file is part of QuantLib, a free-software/open-source library for financial quantitative analysts and developers - https://www.quantlib.org/
#
# QuantLib is free software: you can redistribute it and/or modify it under the
# terms of the QuantLib license. You should have received a copy of the
# license along with this program; if not, please email
# <quantlib-dev@lists.sf.net>. The license is also available online at
# <https://www.quantlib.org/license.shtml>.
#
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the license for more details.
# %% [markdown]
# This notebook only works with Python 3, at least on Travis.
# %%
import sys
if sys.version_info.major < 3:
sys.exit()
# %%
import QuantLib as ql
from matplotlib import pyplot as plt
import numpy as np
import math
# %matplotlib inline
# %%
is_interactive = 'get_ipython' in globals()
# %%
todaysDate = ql.Date(15, ql.May, 2019)
ql.Settings.instance().evaluationDate = todaysDate
# %%
settlementDate = todaysDate + ql.Period(2, ql.Days)
exerciseDate = todaysDate + ql.Period(4, ql.Years)
# %%
dc = ql.Actual365Fixed()
spot = 100
underlying = ql.makeQuoteHandle(spot)
riskFreeRate = ql.YieldTermStructureHandle(ql.FlatForward(settlementDate, 0.05, dc))
dividendYield = ql.YieldTermStructureHandle(ql.FlatForward(settlementDate, 0.025, dc))
vol = 0.30
blackVol = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(settlementDate, ql.TARGET(), vol, dc))
# %%
localVol = ql.LocalVolSurface(
blackVol,
riskFreeRate,
dividendYield,
underlying,
)
hestonProcess = ql.HestonProcess(riskFreeRate, dividendYield, underlying, 0.09, 1.0, 0.06, 0.4, -0.75)
hestonModel = ql.HestonModel(hestonProcess)
# %%
leverageFct = ql.HestonSLVMCModel(
localVol, hestonModel, ql.MTBrownianGeneratorFactory(1234), exerciseDate, 91
).leverageFunction()
# %%
tSteps = 40
uSteps = 30
tv = np.linspace(0.1, dc.yearFraction(settlementDate, exerciseDate), tSteps)
t = np.empty(tSteps * uSteps)
s = np.empty(tSteps * uSteps)
z = np.empty(tSteps * uSteps)
for i in range(0, tSteps):
scale = min(4, math.exp(3 * math.sqrt(tv[i]) * vol))
sv = np.linspace(spot / scale, spot * scale, uSteps)
for j in range(0, uSteps):
idx = i * uSteps + j
t[idx] = tv[i]
s[idx] = math.log(sv[j])
z[idx] = leverageFct.localVol(t[idx], sv[j])
# %%
fig = plt.figure(figsize=(12,8))
ax = plt.axes(projection="3d")
surf = ax.plot_trisurf(s, t, z, cmap=plt.cm.viridis, linewidth=0, antialiased=False, edgecolor="none")
ax.view_init(30, -120)
ax.set_xlabel("ln(S)")
ax.set_ylabel("Time")
ax.text2D(0.225, 0.985, "Leverage Function with $\eta=1.0$", transform=ax.transAxes)
fig.colorbar(surf, shrink=0.75, aspect=14)
plt.show(block=False)
# %% [markdown]
# When this is run as a Python script (i.e., from Travis), we need to close the figure in order to terminate.
# %%
if not is_interactive:
plt.pause(3)
plt.close()
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