An Introduction to C++ Dave Klein Research Analyst Credit Derivatives Research LLC

An Introduction to C++

Dave KleinResearch Analyst

Credit Derivatives Research LLC

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Two Grooks

Problems worthy of attack,prove their worth by hitting back.

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Shun advice at any price, that's what I call good advice.

Piet Hein

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This Session

Overview of C++ Program syntax Classes Pointers Arrays Strings

Using Numerical Recipes Integrating with your project Sample program – Geometric Brownian Motion (if time)

Next Session – using C++ to model a derivative

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Things we won’t cover

Object-oriented Design / Programming The “right” way to do anything

Software developers are fond of having “religious” discussions

In the MFE, there is no time Professional-level programming practice

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C++ Overview

C++ is about 25 years old Originally created as a successor to C

C was created about 35 years ago as a more generic assembly language

C++ is a very “big” language It has many, many features Recommendation: during MFE program, only use

fundamental language features Unless you are an expert, avoid constructs like templates,

polymorphism, operator overloading, multiple inheritance

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C++ Overview con’t

C++ is a “dangerous” language It is easy to introduce bugs It is often difficult to track them downTip: build and test your programs

incrementally

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Language Features – Program Syntax Program Syntax

Functions / methodsLoopsConditional statements

Hopefully, syntax is not completely new to you. If it is, think about using a more familiar computer language.

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...// this is a comment

int myFirstFunction(int a, int b, double c){ int rc = a + b + c;

return rc;}...

Program Syntax (con’t)

Functions

Function nameFunction return type

The function’s code

Return the value

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For loop

Do loop

...for (int i = 0; i < 100; i++){ ... do something ...}...

...i = 0;do{ ... do something ... i++;} while (i < 100);…

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If statement...if (i == 10){ .. do something ..} else { .. do something else}...

IMPORTANT: Note the double equal signs (==) to test for equality

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Classes

Classes provide the basic data/code organization construct within C++

Classes are (roughly) comprised of two parts: Data members (properties) Code members (methods)

Class support inheritance – we don’t have time to cover this Recommendation – if you are not familiar with

inheritance, do not try to learn how to use it during the MFE

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Classes (con’t)class myFirstClass{public:// Some properties int integerProperty; double floatingPointProperty; char characterArray[254];

// some methods // a constructor myFirstClass() { integerProperty = 12; floatingPointProperty = 25.2; strcpy(characterArray, "yo yo yo"); }

// a destructor virtual ~myFirstClass() { }

void doSomething() { ... some code would go here ... }};

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Classes con’t

There are other features to classes including: Information hiding (public, protected, private)Virtual functions

They are extremely powerful and useful, but now is not the time to play with these.

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Classes con’t

Classic interview question: What is the difference between a class and an object?

Better interview question: Can an object ever be a class?

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Pointers

Pointers are a special type of variable Pointers hold the address of data, not the

data Pointers must be assigned values before

they can be used.

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Pointers (con’t)

Pointers are a special type of variable Pointers hold the address of data, not the data

...

int a1; // a1 is not a pointer

int *a2; // a2 is a pointer

a1 = 10;a2 = &a1; // a2 now points to a1

*a2 = 5; // we ‘dereference’ a2 to assign a value

printf("%d %d\n", a1, *a2); // what will this print?

...

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Pointers (con’t)

Be very careful with pointers Someone once estimated that 90% of all C++

bugs can be traced back to bad pointers

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Memory Allocation / Arrays

C++ supports both statically and dynamically allocated arrays

If you dynamically allocate an array, make sure to deallocate it when you are done using it.Make sure you are really done using it before

you deallocate!

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Memory Allocation / Arrays (con’t)

...

int myArray[10]; // this is statically allocated array

for (int i = 0; i < 10; i++){ // Assign a value to each member of the array // Notice that the array is 'referenced' from 0 to 9 // Arrays in C++ 'start' at 0 myArray[i] = i * i + 1;}

...

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Memory Allocation / Arrays (con’t)

...

// this is dynamically allocated array// it looks suspiciously like a pointer!int *myArray;

// first we allocate itmyArray = new int[10];

// this is what a for loop looks likefor (int i = 0; i < 10; i++){ // Assign a value to each member of the array // Notice that the array is 'reference' from 0 to 9 // Arrays in C++ 'start' at 0 myArray[i] = i * i + 1;}

// now we deallocate itdelete[] myArray;

...

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Memory Allocation / Arrays con’t

Question: when should you dynamically allocate an array?

When should static allocation be used?

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Strings (or lack thereof)

C++ does not have a standard string class There is a string class within the Standard Template

Library (STL) Unless you know how to use the STL, ignore it for this

term Recommendation: for output, debugging purposes –

learn how to use printf, sprintf, fprintf The ‘classic’ way of handling strings is to treat them

as arrays of char’s. Then use strcpy, strcmp, etc.

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Strings (or lack thereof) – printf()

printf() enables the formatting of character data

printf(format_string, data1, data2, …)Example:

printf(“This is a %s %d %lf test\n”, “printing”, 2, 5.005)

Produces: This is a printing 2 5.005 test<lf>

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Using Numerical Recipes

There are many numerical libraries available Numerical Recipes for C++ is easy to use DO NOT RE-INVENT THE WHEEL

If you do not have NR, search on-line for numerical class libraries

Do not write your own random-number generator Do not write your own matrix classes Do not implement complex numerical algorithms if there are

“canned” routines already available Exception: if the goal of a homework assignment is to implement

an algorithm.

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Using Numerical Recipes con’t

Warning: there are “Numerical Recipes” books for FORTRAN, C, C++, etc.

Each one is slightly different NR originally implemented in FORTRAN C & C++ versions different enough from

each other to cause problemsFor example, arrays in C version are handled

differently than in C++ version

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Three different ways to add NR to your project1. Recommended : copy the files you need (including

nr.h) to your project directory and add the cpp files to your project

2. Build a static library or DLL with all the NR routines in them

3. Copy the code directly from the NR files into your code files

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Example: Using an NR random number generator

Problem: Want standard normal pseudorandom variable

Solution: use gasdev() from NR

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#include <time.h>#include "nr.h"

...

// let's generate 100 standard normal variablesdouble normals[100];

// seed the random number generatorint idum = -time(NULL);

for (int i = 0; i < 100; i++){ normals[i] = NR::gasdev(idum); }

...

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Putting it All Together – A Geometric Brownian Motion Class We want to:

Model drift, diffusionReuse the same object over and over to

generate different paths

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GBM con’t

Our class properties m_nSInitial – the initial security value (constant) m_nDrift – the drift term (constant) m_nSigma – our volatility term (constant) m_nCurrentTime – the current ‘time’ in our simulation m_nSCurrent – the current security value

Our class methods CGBMotion - our constructor void step – moves time forward double getCurrentValue – returns m_nSCurrent void reset - resets current time & security value

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Code #include <math.h>#include "nr.h"

class CGBMotion{public: // our properties

int m_nIdum; // used by NR::gasdevdouble m_nSInitial; // initial security value (constant)double m_nDrift; // our drift (constant)double m_nSigma; // our volatility (constant)double m_nCurrentTime; // the current elapsed timedouble m_nCurrentDiffusion; // how much the process has diffused

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Code con’t . . . public:// our constructorCGBMotion(double nSInitial, double nDrift, double nSigma, int seed){

m_nSInitial = nSInitial;m_nDrift = nDrift;m_nSigma = nSigma;m_nCurrentTime = 0;m_nCurrentDiffusion = 0;m_nIdum = seed;

}

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Code con’t . . .

void step(double nTime){ double nDeltaT = nTime - m_nCurrentTime; // how much time has elapsed? if (nDeltaT > 0) {

// some time has elapsed// add to our diffusion relative to sqrt of elapsed timem_nCurrentDiffusion += sqrt(nDeltaT) * NR::gasdev(m_nIdum);

// update our current timem_nCurrentTime = nTime;

}}

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Code con’t . . .

double getCurrentValue(){

return m_nSInitial * exp(m_nDrift*m_nCurrentTime - .5* m_nSigma * m_nSigma*m_nCurrentTime + m_nSigma*m_nCurrentDiffusion)

);}

double reset(){

m_nCurrentTime = 0;m_nCurrentDiffusion = 0;

}

};

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GBM Sample Programint main(int argc, char* argv[]){ CGBMotion oGBM(100.0, .05, .2, -10); // our brownian motion object

// run 10000 simulations for (int i = 0; i < 10000; i++) { double t = 0; oGBM.reset();

// run 100 time steps for (int j = 0; j < 100; j++) { t = t + .01; oGBM.step(t); }

// print the results printf("%02d: Simulated value %lf\n", i, oGBM.getCurrentValue()); }

return 0;}

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3 Great Resources

Wikipedia: http://www.wikipedia.org Wilmott: http://www.wilmott.com Google (of course) :

http://www.google.com

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Questions / Discussion

Documents

An Introduction to C++ Dave Klein Research Analyst Credit Derivatives Research LLC