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Python 在科学计算、数据分析和可视化等方面已经形成了非常强大的生态。而且,作为一门时尚的脚本语言,易学易用。因此,对于量化分析和风险管理的从业者来说,将某些 QuantLib 的历史代码转换成 Python 程序是一件值得尝试的工作。
Python 本身的面向对象机制非常完善,借助 SWIG 的包装,由 C++ 代码转换而成的 Python 程序基本上可以完整地保留原本的类架构。对于用户来说,应用层面的历史代码几乎可以平行的进行移植,只需稍加修改即可。
本文将以 QuantLib 官方网站上的 EquityOption.cpp 为例,展示如何将应用层面的 C++ 代码转换成 Python 程序,并总结出一般的转换方法和注意事项。
下面,我将逐句把 C++ 代码改写成 Python 程序。
C++ 代码:
#include <ql/qldefines.hpp>
#ifdef BOOST_MSVC
# include <ql/auto_link.hpp>
#endif
#include <ql/instruments/vanillaoption.hpp>
#include <ql/pricingengines/vanilla/binomialengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/pricingengines/vanilla/baroneadesiwhaleyengine.hpp>
#include <ql/pricingengines/vanilla/bjerksundstenslandengine.hpp>
#include <ql/pricingengines/vanilla/batesengine.hpp>
#include <ql/pricingengines/vanilla/integralengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeanengine.hpp>
#include <ql/pricingengines/vanilla/mcamericanengine.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <iostream>
#include <iomanip>
using namespace QuantLib;
#if defined(QL_ENABLE_SESSIONS)
namespace QuantLib {
Integer sessionId() { return 0; }
}
#endif
Python 代码:
import QuantLib as ql
import prettytable as pt
首先,引入必要的模块,对 C++ 来说是一组头文件。Python 的优势显而易见。
C++ 代码:
// set up dates
Calendar calendar = TARGET();
Date todaysDate(15, May, 1998);
Date settlementDate(17, May, 1998);
Settings::instance().evaluationDate() = todaysDate;
Python 代码:
# set up dates
calendar = ql.TARGET()
todaysDate = ql.Date(15, ql.May, 1998)
settlementDate = ql.Date(17, ql.May, 1998)
ql.Settings.instance().evaluationDate = todaysDate
C++ 中对象的声明有两种常见的方式:
BaseClass object = Class(...)
,其中 Class
可以是 BaseClass
本身,或者其派生类。示例中的 TARGET
正是 Calendar
的派生类;Class object(...)
。Python 中无需声明对象类型,而是以赋值的形式创建一个对象,所以对于上述两类格式的代码,统一改写成 object = Class(...)
。
经验 1:对象声明语句
BaseClass object = Class(...)
和Class object(...)
统一改写成object = Class(...)
。
Settings
是 QuantLib 中的一个“单体模式”的实现,通常用来为整个程序设置统一的估值日期,几乎每个应用程序中都会出现。通过调用 Settings
的静态方法 instance()
,用户可以修改单体实例的某些属性,其中 evaluationDate()
方法可以把存储估值日期的成员变量地址暴露出来,让用户进行设置。
不过,Python 中的类没有 ::
运算符,类的方法也不能暴露成员变量的地址。所以,原本的静态方法一律通过 .
运算符调用,同时 evaluationDate()
方法被重定义为类的 property
,这就是为什么 Python 语句中 evaluationDate
后面没有 ()
。注意,instance()
后面的 ()
不能丢。
经验 2:用来对
Settings::instance()
进行配置的成员函数,例如evaluationDate()
,在 Python 中以类的property
形式出现,不过名称不变。
// our options
Option::Type type(Option::Put);
Real underlying = 36;
Real strike = 40;
Spread dividendYield = 0.00;
Rate riskFreeRate = 0.06;
Volatility volatility = 0.20;
Date maturity(17, May, 1999);
DayCounter dayCounter = Actual365Fixed();
Python 代码:
# our options
optType = ql.Option.Put
underlying = 36.0
strike = 40.0
dividendYield = 0.00
riskFreeRate = 0.06
volatility = 0.20
maturity = ql.Date(17, ql.May, 1999)
dayCounter = ql.Actual365Fixed()
C++ 中类内部枚举类型的对象声明和类对象声明相似,采用 Class::Enum object(Class::element)
的形式。枚举元素本质上是一些整数常量。
SWIG 在包装 QuantLib 的 Python 接口时会把 C++ 类内部的枚举类型转换成 Python 类中的公有属性,其值依然是一些整数值。所以,枚举类型对象的声明就直接改写成赋值语句。因此,Class::Enum object(Class::element)
语句统一改写成 object = Class.element
。
示例中的 Type
是 Option
类内部的一个枚举型,而 Put
是 Type
中的一个元素,另一个是 Call
。因为 type
是 Python 的关键字,改写时一定要重命名。
经验 3:对于类中的枚举类型,
Class::Enum object(Class::element)
语句统一改写成object = Class.element
。
对于基本类型(整数、浮点数、字符、字符串)来说,改写非常容易。由于 Python 无需声明类型,Type object = value
语句统一改写成赋值语句——object = value
。
经验 4:对于基本类型,
Type object = value
语句统一改写成object = value
。
C++ 代码:
std::cout << "Option type = " << type << std::endl;
std::cout << "Maturity = " << maturity << std::endl;
std::cout << "Underlying price = " << underlying << std::endl;
std::cout << "Strike = " << strike << std::endl;
std::cout << "Risk-free interest rate = " << io::rate(riskFreeRate) << std::endl;
std::cout << "Dividend yield = " << io::rate(dividendYield) << std::endl;
std::cout << "Volatility = " << io::volatility(volatility) << std::endl;
std::cout << std::endl;
std::string method;
std::cout << std::endl ;
// write column headings
Size widths[] = { 35, 14, 14, 14 };
std::cout << std::setw(widths[0]) << std::left << "Method"
<< std::setw(widths[1]) << std::left << "European"
<< std::setw(widths[2]) << std::left << "Bermudan"
<< std::setw(widths[3]) << std::left << "American"
<< std::endl;
Python 代码:
print(‘Option type =‘, optType)
print(‘Maturity =‘, maturity)
print(‘Underlying price =‘, underlying)
print(‘Strike =‘, strike)
print(‘Risk-free interest rate =‘, ‘{0:%}‘.format(riskFreeRate))
print(‘Dividend yield =‘, ‘{0:%}‘.format(dividendYield))
print(‘Volatility =‘, ‘{0:%}‘.format(volatility))
print()
# show table
tab = pt.PrettyTable([‘Method‘, ‘European‘, ‘Bermudan‘, ‘American‘])
字符串输出部分没什么好说的,我使用了 prettytable
包来美化输出结果。
C++ 代码:
std::vector<Date> exerciseDates;
for (Integer i = 1; i <= 4; i++)
exerciseDates.push_back(settlementDate + 3 * i * Months);
Python 代码:
exerciseDates = ql.DateVector()
for i in range(1, 5):
exerciseDates.push_back(settlementDate + ql.Period(3 * i, ql.Months))
Python 本身没有“模板”的概念,因此 SWIG 只能对模板的实例化进行包装(模板的实例化就是一个具体的类),进而得到一些 Python 类。对于某些常用类型,例如 Date
,QuantLib 的 Python 接口包装了对应的 std::vector
模板的实例化,包装后得到的 Python 类有一致的命名格式——ClassVector
,对于 std::vector<Date>
而言就是 DateVector
。
因为模板的实例化实际上就是一个具体的类,因此,这部分代码的改写方法遵循经验 1。
和 C++ 完全不同,Python 不是一个“强类型”的语言,在改写涉及隐式转换的代码时要格外注意。Months
是 QuantLib 中的枚举类型 TimeUnit
的元素,SWIG 在包装枚举类型时会将元素转换成 Python 中的整数,丢失了 TimeUnit
的类型信息。由于 Python 不是强类型的,被包装的枚举类型会丢失类型信息,因此,3 * i * Months
在 C++ 中可以顺利地隐式转换成一个 Period
对象——Period(3 * i, Months)
,但是,在 Python 中 3 * i * Months
只会被当做三个整数相乘。此时,3 * i * Months
必须改写成显式声明的格式——ql.Period(3 * i, ql.Months)
。
经验 5:隐式转换成
Period
对象的代码在改写时要改成显式声明的格式,这类代码通常与枚举类型TimeUnit
有关。
C++ 代码:
ext::shared_ptr<Exercise> europeanExercise(
new EuropeanExercise(maturity));
ext::shared_ptr<Exercise> bermudanExercise(
new BermudanExercise(exerciseDates));
ext::shared_ptr<Exercise> americanExercise(
new AmericanExercise(settlementDate, maturity));
Python 代码:
europeanExercise = ql.EuropeanExercise(maturity)
bermudanExercise = ql.BermudanExercise(exerciseDates)
americanExercise = ql.AmericanExercise(settlementDate, maturity)
C++ 中声明智能指针的最常见方式是:shared_ptr<BaseClass> object(new Class(...))
(shared_ptr
也是最常用的智能指针类模板),其中 Class
可以是 BaseClass
本身,或者其派生类。示例中的 EuropeanExercise
正是 Exercise
的派生类。这类代码在 Python 中统一改写成声明对象的形式——object = Class(...)
,因为智能指针通常被视为一个对象。
经验 6:对于智能指针,
shared_ptr<BaseClass> object(new Class(...))
统一改写成object = Class(...)
。
C++ 代码:
Handle<Quote> underlyingH(
ext::shared_ptr<Quote>(new SimpleQuote(underlying)));
Python 代码:
underlyingH = ql.QuoteHandle(ql.SimpleQuote(underlying))
Quote
类和 Handle
模板是 QuantLib 中最常用到的两个类(模板),它们通常充当“观察者模式”中被观察的一方,一般被当做参数来配置更复杂类的实例。Quote
类接受一个浮点数做参数,而 Handle
模板接受一个智能指针。当用户修改 Quote
实例的值,或 Handle
实例指向的指针之后,那些接受过这些实例的复杂类对象会接到通知,并自动触发相关计算。这个机制非常赞!
关于 Quote
的具体使用案例,详情可以参考《Quote
带来的便利》。
QuantLib 的 Python 接口已经包装了 Handle
模板的一些实例化,例如 QuoteHandle
和下面将要看到的 YieldTermStructureHandle
,这些类有一致的命名格式——ClassHandle
。
还是那句话,C++ 模板的实例化实际上就是一个具体的类,因此,这部分代码的改写方法遵循经验 1 和经验 6。
C++ 代码:
// bootstrap the yield/dividend/vol curves
Handle<YieldTermStructure> flatTermStructure(
ext::shared_ptr<YieldTermStructure>(
new FlatForward(settlementDate, riskFreeRate, dayCounter)));
Handle<YieldTermStructure> flatDividendTS(
ext::shared_ptr<YieldTermStructure>(
new FlatForward(settlementDate, dividendYield, dayCounter)));
Handle<BlackVolTermStructure> flatVolTS(
ext::shared_ptr<BlackVolTermStructure>(
new BlackConstantVol(
settlementDate, calendar, volatility, dayCounter)));
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> bsmProcess(
new BlackScholesMertonProcess(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS));
// options
VanillaOption europeanOption(payoff, europeanExercise);
VanillaOption bermudanOption(payoff, bermudanExercise);
VanillaOption americanOption(payoff, americanExercise);
// Analytic formulas:
// Black-Scholes for European
method = "Black-Scholes";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new AnalyticEuropeanEngine(bsmProcess)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// semi-analytic Heston for European
method = "Heston semi-analytic";
ext::shared_ptr<HestonProcess> hestonProcess(
new HestonProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility, 0.001, 0.0));
ext::shared_ptr<HestonModel> hestonModel(
new HestonModel(hestonProcess));
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new AnalyticHestonEngine(hestonModel)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// semi-analytic Bates for European
method = "Bates semi-analytic";
ext::shared_ptr<BatesProcess> batesProcess(
new BatesProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility,
0.001, 0.0, 1e-14, 1e-14, 1e-14));
ext::shared_ptr<BatesModel> batesModel(
new BatesModel(batesProcess));
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(new BatesEngine(batesModel)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Barone-Adesi and Whaley approximation for American
method = "Barone-Adesi/Whaley";
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BaroneAdesiWhaleyApproximationEngine(bsmProcess)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Bjerksund and Stensland approximation for American
method = "Bjerksund/Stensland";
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BjerksundStenslandApproximationEngine(bsmProcess)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Integral
method = "Integral";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new IntegralEngine(bsmProcess)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Finite differences
Size timeSteps = 801;
method = "Finite differences";
ext::shared_ptr<PricingEngine> fdengine =
ext::make_shared<FdBlackScholesVanillaEngine>(
bsmProcess, timeSteps, timeSteps - 1);
europeanOption.setPricingEngine(fdengine);
bermudanOption.setPricingEngine(fdengine);
americanOption.setPricingEngine(fdengine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
Python 代码:
# bootstrap the yield/dividend/vol curves
flatTermStructure = ql.YieldTermStructureHandle(
ql.FlatForward(settlementDate, riskFreeRate, dayCounter))
flatDividendTS = ql.YieldTermStructureHandle(
ql.FlatForward(settlementDate, dividendYield, dayCounter))
flatVolTS = ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
settlementDate, calendar, volatility, dayCounter))
payoff = ql.PlainVanillaPayoff(optType, strike)
bsmProcess = ql.BlackScholesMertonProcess(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS)
# options
europeanOption = ql.VanillaOption(payoff, europeanExercise)
bermudanOption = ql.VanillaOption(payoff, bermudanExercise)
americanOption = ql.VanillaOption(payoff, americanExercise)
# Analytic formulas:
# Black-Scholes for European
method = ‘Black-Scholes‘
europeanOption.setPricingEngine(
ql.AnalyticEuropeanEngine(bsmProcess))
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# semi-analytic Heston for European
method = ‘Heston semi-analytic‘
hestonProcess = ql.HestonProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility, 0.001, 0.0)
hestonModel = ql.HestonModel(hestonProcess)
europeanOption.setPricingEngine(
ql.AnalyticHestonEngine(hestonModel))
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# semi-analytic Bates for European
method = ‘Bates semi-analytic‘
batesProcess = ql.BatesProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility,
0.001, 0.0, 1e-14, 1e-14, 1e-14)
batesModel = ql.BatesModel(batesProcess)
europeanOption.setPricingEngine(
ql.BatesEngine(batesModel))
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# Barone-Adesi and Whaley approximation for American
method = ‘Barone-Adesi/Whaley‘
americanOption.setPricingEngine(
ql.BaroneAdesiWhaleyEngine(bsmProcess))
tab.add_row([method, ‘N/A‘, ‘N/A‘, americanOption.NPV()])
# Bjerksund and Stensland approximation for American
method = ‘Bjerksund/Stensland‘
americanOption.setPricingEngine(
ql.BjerksundStenslandEngine(bsmProcess))
tab.add_row([method, ‘N/A‘, ‘N/A‘, americanOption.NPV()])
# Integral
method = ‘Integral‘
europeanOption.setPricingEngine(
ql.IntegralEngine(bsmProcess))
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# Finite differences
timeSteps = 801
method = ‘Finite differences‘
fdengine = ql.FdBlackScholesVanillaEngine(bsmProcess, timeSteps, timeSteps - 1)
europeanOption.setPricingEngine(fdengine)
bermudanOption.setPricingEngine(fdengine)
americanOption.setPricingEngine(fdengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
这部分代码的改写没什么新意,需要注意的是,某些非模板类在被包装时会被重命名,例如 BaroneAdesiWhaleyApproximationEngine
被重命名为 BaroneAdesiWhaleyEngine
。如果用户根据前面的 6 条经验找不到 Python 接口中的对应物,那么,要改写的 C++ 代码可能遇到了重命名的情况。这时,用户需要到 QuantLib-SWIG 的接口文件中查找 C++ 类(结构体)或函数,看看有没有被重命名。继续前面的例子,SWIG 代码 %rename(BaroneAdesiWhaleyEngine) BaroneAdesiWhaleyApproximationEngine;
表明 BaroneAdesiWhaleyApproximationEngine
被重命名为 BaroneAdesiWhaleyEngine
。
经验 7:疑似遇到重命名的情况(常见于名字特别长的类),到 QuantLib-SWIG 的接口文件中查找重命名命令。
C++ 代码:
// Binomial method: Jarrow-Rudd
method = "Binomial Jarrow-Rudd";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Cox-Ross-Rubinstein
method = "Binomial Cox-Ross-Rubinstein";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Additive equiprobabilities
method = "Additive equiprobabilities";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<AdditiveEQPBinomialTree>(
bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<AdditiveEQPBinomialTree>(
bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<AdditiveEQPBinomialTree>(
bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Trigeorgis
method = "Binomial Trigeorgis";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Tian
method = "Binomial Tian";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Leisen-Reimer
method = "Binomial Leisen-Reimer";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Joshi
method = "Binomial Joshi";
europeanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps)));
bermudanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps)));
americanOption.setPricingEngine(
ext::shared_ptr<PricingEngine>(
new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps)));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
Python 代码:
# Binomial method: Jarrow-Rudd
method = ‘Binomial Jarrow-Rudd‘
jrengine = ql.BinomialJRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(jrengine)
bermudanOption.setPricingEngine(jrengine)
americanOption.setPricingEngine(jrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Cox-Ross-Rubinstein
method = ‘Binomial Cox-Ross-Rubinstein‘
crrengine = ql.BinomialCRRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(crrengine)
bermudanOption.setPricingEngine(crrengine)
americanOption.setPricingEngine(crrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Additive equiprobabilities
method = ‘Additive equiprobabilities‘
eqpengine = ql.BinomialEQPVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(eqpengine)
bermudanOption.setPricingEngine(eqpengine)
americanOption.setPricingEngine(eqpengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Trigeorgis
method = ‘Binomial Trigeorgis‘
trengine = ql.BinomialTrigeorgisVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(trengine)
bermudanOption.setPricingEngine(trengine)
americanOption.setPricingEngine(trengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Tian
method = ‘Binomial Tian‘
tiengine = ql.BinomialTianVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(tiengine)
bermudanOption.setPricingEngine(tiengine)
americanOption.setPricingEngine(tiengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Leisen-Reimer
method = ‘Binomial Leisen-Reimer‘
lrengine = ql.BinomialLRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(lrengine)
bermudanOption.setPricingEngine(lrengine)
americanOption.setPricingEngine(lrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Joshi
method = ‘Binomial Joshi‘
j4engine = ql.BinomialJ4VanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(j4engine)
bermudanOption.setPricingEngine(j4engine)
americanOption.setPricingEngine(j4engine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
对于 C++ 中的模板,SWIG 在包装 Python 接口时只包装模板的实例化,并且会为模板的实例化取一个新名字。这时,用户需要到 QuantLib-SWIG 的接口文件中查找模板的实例化,看看取了什么新名字。继续前面的例子,SWIG 代码 %template(BinomialJRVanillaEngine) BinomialVanillaEngine<JarrowRudd>;
表示 BinomialVanillaEngine<JarrowRudd>
在 Python 中对应的类叫做 BinomialJRVanillaEngine
。
经验 8:遇到模板实例化的情况,到 QuantLib-SWIG 的接口文件中查找实例化后新的类名。
C++ 代码:
// Monte Carlo Method: MC (crude)
timeSteps = 1;
method = "MC (crude)";
Size mcSeed = 42;
ext::shared_ptr<PricingEngine> mcengine1;
mcengine1 = MakeMCEuropeanEngine<PseudoRandom>(
bsmProcess)
.withSteps(timeSteps)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed);
europeanOption.setPricingEngine(mcengine1);
// Real errorEstimate = europeanOption.errorEstimate();
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Monte Carlo Method: QMC (Sobol)
method = "QMC (Sobol)";
Size nSamples = 32768; // 2^15
ext::shared_ptr<PricingEngine> mcengine2;
mcengine2 = MakeMCEuropeanEngine<LowDiscrepancy>(
bsmProcess)
.withSteps(timeSteps)
.withSamples(nSamples);
europeanOption.setPricingEngine(mcengine2);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Monte Carlo Method: MC (Longstaff Schwartz)
method = "MC (Longstaff Schwartz)";
ext::shared_ptr<PricingEngine> mcengine3;
mcengine3 = MakeMCAmericanEngine<PseudoRandom>(
bsmProcess)
.withSteps(100)
.withAntitheticVariate()
.withCalibrationSamples(4096)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed);
americanOption.setPricingEngine(mcengine3);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
Python 代码:
timeSteps = 1
# Monte Carlo Method: MC (crude)
method = ‘MC (crude)‘
mcSeed = 42
mcengine1 = ql.MCPREuropeanEngine(
bsmProcess,
timeSteps=timeSteps,
requiredTolerance=0.02,
seed=mcSeed)
europeanOption.setPricingEngine(mcengine1)
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# Monte Carlo Method: QMC (Sobol)
method = ‘QMC (Sobol)‘
nSamples = 32768 # 2^15
mcengine2 = ql.MCLDEuropeanEngine(
bsmProcess,
timeSteps=timeSteps,
requiredSamples=nSamples)
europeanOption.setPricingEngine(mcengine2)
tab.add_row([method, europeanOption.NPV(), ‘N/A‘, ‘N/A‘])
# Monte Carlo Method: MC (Longstaff Schwartz)
method = ‘MC (Longstaff Schwartz)‘
mcengine3 = ql.MCPRAmericanEngine(
bsmProcess,
timeSteps=100,
antitheticVariate=True,
nCalibrationSamples=4096,
requiredTolerance=0.02,
seed=mcSeed)
americanOption.setPricingEngine(mcengine3)
tab.add_row([method, ‘N/A‘, ‘N/A‘, americanOption.NPV()])
tab.float_format = ‘.6‘
tab.align = ‘l‘
print(tab)
MakeMCEuropeanEngine<PseudoRandom>
是 QuantLib 中工厂模式的一个实现,对于拥有较多默认参数的类,QuantLib 会提供一个对应的工厂类,用户借助工厂类“制造”一个半成品对象,并通过一组成员函数以流水线的方式配置这个半成品的参数,以实现对默认参数的灵活配置。这些流水线函数有一致的命名格式——withArgument
,Argument
通常是某个默认参数的名字。这套机制也被称为“命名参数惯用法”。这些工厂类有一致的命名规范——MakeClass
,其中 Class
是一个类的名字或实例化的模板,MakeClass
将制造出一个 Class
对象。
Python 中存在“关键字参数”的机制,因此,上述“流水线函数”显得非常笨拙,对于这类代码的改写,用户只要知道“MakeClass
将制造出一个 Class
对象”这一点,并理解流水线函数所配置的参数,然后应用前面总结的 8 条经验就可以成功改写。
经验 9:名为
MakeClass
的工厂类将制造出一个Class
对象,后续的成员函数表示配置的参数。
C++ 代码运行结果:
Option type = Put
Maturity = May 17th, 1999
Underlying price = 36
Strike = 40
Risk-free interest rate = 6.000000 %
Dividend yield = 0.000000 %
Volatility = 20.000000 %
Method European Bermudan American
Black-Scholes 3.844308 N/A N/A
Heston semi-analytic 3.844306 N/A N/A
Bates semi-analytic 3.844306 N/A N/A
Barone-Adesi/Whaley N/A N/A 4.459628
Bjerksund/Stensland N/A N/A 4.453064
Integral 3.844309 N/A N/A
Finite differences 3.844330 4.360765 4.486113
Binomial Jarrow-Rudd 3.844132 4.361174 4.486552
Binomial Cox-Ross-Rubinstein 3.843504 4.360861 4.486415
Additive equiprobabilities 3.836911 4.354455 4.480097
Binomial Trigeorgis 3.843557 4.360909 4.486461
Binomial Tian 3.844171 4.361176 4.486413
Binomial Leisen-Reimer 3.844308 4.360713 4.486076
Binomial Joshi 3.844308 4.360713 4.486076
MC (crude) 3.834522 N/A N/A
QMC (Sobol) 3.844613 N/A N/A
MC (Longstaff Schwartz) N/A N/A 4.456935
Python 程序运行结果:
Option type = -1
Maturity = May 17th, 1999
Underlying price = 36.0
Strike = 40.0
Risk-free interest rate = 6.000000%
Dividend yield = 0.000000%
Volatility = 20.000000%
+------------------------------+----------+----------+----------+
| Method | European | Bermudan | American |
+------------------------------+----------+----------+----------+
| Black-Scholes | 3.844308 | N/A | N/A |
| Heston semi-analytic | 3.844306 | N/A | N/A |
| Bates semi-analytic | 3.844306 | N/A | N/A |
| Barone-Adesi/Whaley | N/A | N/A | 4.459628 |
| Bjerksund/Stensland | N/A | N/A | 4.453064 |
| Integral | 3.844309 | N/A | N/A |
| Finite differences | 3.844330 | 4.360765 | 4.486113 |
| Binomial Jarrow-Rudd | 3.844132 | 4.361174 | 4.486552 |
| Binomial Cox-Ross-Rubinstein | 3.843504 | 4.360861 | 4.486415 |
| Additive equiprobabilities | 3.836911 | 4.354455 | 4.480097 |
| Binomial Trigeorgis | 3.843557 | 4.360909 | 4.486461 |
| Binomial Tian | 3.844171 | 4.361176 | 4.486413 |
| Binomial Leisen-Reimer | 3.844308 | 4.360713 | 4.486076 |
| Binomial Joshi | 3.844308 | 4.360713 | 4.486076 |
| MC (crude) | 3.834522 | N/A | N/A |
| QMC (Sobol) | 3.844613 | N/A | N/A |
| MC (Longstaff Schwartz) | N/A | N/A | 4.456935 |
+------------------------------+----------+----------+----------+
完全一样!
BaseClass object = Class(...)
和 Class object(...)
统一改写成 object = Class(...)
。Settings::instance()
进行配置的成员函数,例如 evaluationDate()
,在 Python 中以类的 property
形式出现,不过名称不变。Class::Enum object(Class::element)
语句统一改写成 object = Class.element
。Type object = value
语句统一改写成 object = value
。Period
对象的代码在改写时要改成显式声明的格式,这类代码通常与枚举类型 TimeUnit
有关。shared_ptr<BaseClass> object(new Class(...))
统一改写成 object = Class(...)
。MakeClass
的工厂类将制造出一个 Class
对象,后续的成员函数表示配置的参数。需要注意的是,QuantLib 中并非所有的功能都有对应的 Python 接口,如果用户需要的功能未被包装,用户只好修改 SWIG 代码,自行生成 Python 接口,可以参考一下文章:
QuantLib 金融计算——C++ 代码改写成 Python 程序的一些经验
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原文地址:https://www.cnblogs.com/xuruilong100/p/13281006.html