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# ---
# jupyter:
# jupytext:
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# text_representation:
# extension: .py
# format_name: percent
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# jupytext_version: 1.4.2
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# display_name: Python 3
# language: python
# name: python3
# ---
# %% [markdown]
# # European options
#
# Copyright (©) 2004, 2005, 2006, 2007 StatPro Italia srl
#
# 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.
# %%
import QuantLib as ql
import pandas as pd
# %% [markdown]
# ### Global parameters
# %%
todaysDate = ql.Date(15, ql.May, 1998)
ql.Settings.instance().evaluationDate = todaysDate
# %%
interactive = 'get_ipython' in globals()
# %% [markdown]
# ### Option construction
# %%
exercise = ql.EuropeanExercise(ql.Date(17, ql.May, 1999))
payoff = ql.PlainVanillaPayoff(ql.Option.Call, 8.0)
# %%
option = ql.VanillaOption(payoff, exercise)
# %% [markdown]
# ### Market data
# %%
underlying = ql.SimpleQuote(7.0)
dividendYield = ql.FlatForward(todaysDate, 0.05, ql.Actual365Fixed())
volatility = ql.BlackConstantVol(todaysDate, ql.TARGET(), 0.10, ql.Actual365Fixed())
riskFreeRate = ql.FlatForward(todaysDate, 0.05, ql.Actual365Fixed())
# %% [markdown]
# ### Processes and models
# %%
process = ql.BlackScholesMertonProcess(
ql.QuoteHandle(underlying),
ql.YieldTermStructureHandle(dividendYield),
ql.YieldTermStructureHandle(riskFreeRate),
ql.BlackVolTermStructureHandle(volatility),
)
# %%
hestonProcess = ql.HestonProcess(
ql.YieldTermStructureHandle(riskFreeRate),
ql.YieldTermStructureHandle(dividendYield),
ql.QuoteHandle(underlying),
0.1 * 0.1,
1.0,
0.1 * 0.1,
0.0001,
0.0,
)
hestonModel = ql.HestonModel(hestonProcess)
# %% [markdown]
# ### Pricing
#
# We'll collect tuples of method name, option value, estimated error, and discrepancy from the analytic formula.
# %%
results = []
# %% [markdown]
# #### Analytic formula
# %%
option.setPricingEngine(ql.AnalyticEuropeanEngine(process))
value = option.NPV()
refValue = value
results.append(('Analytic', value, None, None))
# %% [markdown]
# #### Heston semi-analytic formula
# %%
option.setPricingEngine(ql.AnalyticHestonEngine(hestonModel))
value = option.NPV()
results.append(('Heston analytic', value, None, abs(value - refValue)))
# %% [markdown]
# #### Heston COS method
# %%
option.setPricingEngine(ql.COSHestonEngine(hestonModel))
value = option.NPV()
results.append(('Heston COS', value, None, abs(value - refValue)))
# %% [markdown]
# #### Integral method
# %%
option.setPricingEngine(ql.IntegralEngine(process))
value = option.NPV()
results.append(('Integral', value, None, abs(value - refValue)))
# %% [markdown]
# #### Finite-difference method
# %%
timeSteps = 801
gridPoints = 800
# %%
option.setPricingEngine(ql.FdBlackScholesVanillaEngine(process, timeSteps, gridPoints))
value = option.NPV()
results.append(('Finite diff.', value, None, abs(value - refValue)))
# %% [markdown]
# #### Binomial method
# %%
timeSteps = 801
# %%
for tree in ["JR", "CRR", "EQP", "Trigeorgis", "Tian", "LR", "Joshi4"]:
option.setPricingEngine(ql.BinomialVanillaEngine(process, tree, timeSteps))
value = option.NPV()
results.append(('Binomial (%s)' % tree, value, None, abs(value - refValue)))
# %% [markdown]
# #### Monte Carlo method
# %%
option.setPricingEngine(ql.MCEuropeanEngine(process, "pseudorandom", timeSteps=1,
requiredTolerance=0.02, seed=42))
value = option.NPV()
results.append(("Monte Carlo (pseudo-random)", value, option.errorEstimate(), abs(value - refValue)))
# %%
option.setPricingEngine(ql.MCEuropeanEngine(process, "lowdiscrepancy", timeSteps=1,
requiredSamples=32768))
value = option.NPV()
results.append(("Monte Carlo (low-discrepancy)", value, None, abs(value - refValue)))
# %% [markdown]
# ### Results
# %%
df = pd.DataFrame(results,
columns=["Method", "Option value", "Error estimate", "Actual error"])
# %%
df.style.hide(axis="index")
# %% [markdown]
# The following displays the results when this is run as a Python script (in which case the cell above is not displayed).
# %%
if not interactive:
print(df)
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