python代码改写_QuantLib 金融计算——C++ 代码改写成 Python 程序的一些经验

QuantLib 金融计算——C++ 代码改写成 Python 程序的一些经验

概述

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。

python代码改写_QuantLib 金融计算——C++ 代码改写成 Python 程序的一些经验_第1张图片

将 C++ 代码改写成 Python 程序

下面,我将逐句把 C++ 代码改写成 Python 程序。

C++ 代码:

#include

#ifdef BOOST_MSVC

# include

#endif

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

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。

C++ 代码:

// 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 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 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 europeanExercise(

new EuropeanExercise(maturity));

ext::shared_ptr bermudanExercise(

new BermudanExercise(exerciseDates));

ext::shared_ptr 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 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 object(new Class(...)) 统一改写成 object = Class(...)。

C++ 代码:

Handle underlyingH(

ext::shared_ptr(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 flatTermStructure(

ext::shared_ptr(

new FlatForward(settlementDate, riskFreeRate, dayCounter)));

Handle flatDividendTS(

ext::shared_ptr(

new FlatForward(settlementDate, dividendYield, dayCounter)));

Handle flatVolTS(

ext::shared_ptr(

new BlackConstantVol(

settlementDate, calendar, volatility, dayCounter)));

ext::shared_ptr payoff(

new PlainVanillaPayoff(type, strike));

ext::shared_ptr 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(

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(

new HestonProcess(

flatTermStructure, flatDividendTS, underlyingH,

volatility * volatility, 1.0, volatility * volatility, 0.001, 0.0));

ext::shared_ptr hestonModel(

new HestonModel(hestonProcess));

europeanOption.setPricingEngine(

ext::shared_ptr(

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(

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(

new BatesModel(batesProcess));

europeanOption.setPricingEngine(

ext::shared_ptr(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(

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(

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(

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 fdengine =

ext::make_shared(

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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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(

new BinomialVanillaEngine(

bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(

bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(

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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

bermudanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(bsmProcess, timeSteps)));

americanOption.setPricingEngine(

ext::shared_ptr(

new BinomialVanillaEngine(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; 表示 BinomialVanillaEngine 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 mcengine1;

mcengine1 = MakeMCEuropeanEngine(

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 mcengine2;

mcengine2 = MakeMCEuropeanEngine(

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 mcengine3;

mcengine3 = MakeMCAmericanEngine(

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 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。

对比结果

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!

总结

经验 1:对象声明语句 BaseClass object = Class(...) 和 Class object(...) 统一改写成 object = Class(...)。

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。

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。

经验 4:对于基本类型,Type object = value 语句统一改写成 object = value。

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。

经验 6:对于智能指针,shared_ptr object(new Class(...)) 统一改写成 object = Class(...)。

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。

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。

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。

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:

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