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

2. 2 Two Grooks Problems worthy of attack, prove their worth by hitting back. ------ Shun advice at any price, that's what I call good advice. Piet Hein

3. 3 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

4. 4 Things we wont 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

5. 5 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

6. 6 C++ Overview cont C++ is a dangerous language It is easy to introduce bugs It is often difficult to track them down Tip: build and test your programs incrementally

7. 7 Language Features – Program Syntax Program Syntax Functions / methods Loops Conditional statements Hopefully, syntax is not completely new to you. If it is, think about using a more familiar computer language.

8. 8... // this is a comment int myFirstFunction(int a, int b, double c) { int rc = a + b + c; return rc; }... Program Syntax (cont) Functions Function name Function return type The functions code Return the value

9. 9 Program Syntax (cont) For loop Do loop... for (int i = 0; i < 100; i++) {... do something... }... i = 0; do {... do something... i++; } while (i < 100); …

10. 10 Program Syntax (cont) If statement... if (i == 10) {.. do something.. } else {.. do something else }... IMPORTANT: Note the double equal signs (==) to test for equality

11. 11 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 dont 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

12. 12 Classes (cont) 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... } };

13. 13 Classes cont 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.

14. 14 Classes cont Classic interview question: What is the difference between a class and an object? Better interview question: Can an object ever be a class?

15. 15 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.

16. 16 Pointers (cont) 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?...

17. 17 Pointers (cont) Be very careful with pointers Someone once estimated that 90% of all C++ bugs can be traced back to bad pointers

18. 18 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!

19. 19 Memory Allocation / Arrays (cont)... 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; }...

20. 20 Memory Allocation / Arrays (cont)... // this is dynamically allocated array // it looks suspiciously like a pointer! int *myArray; // first we allocate it myArray = new int[10]; // this is what a for loop looks like for (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 it delete[] myArray;...

21. 21 Memory Allocation / Arrays cont Question: when should you dynamically allocate an array? When should static allocation be used?

22. 22 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 chars. Then use strcpy, strcmp, etc.

23. 23 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

24. 24 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.

25. 25 Using Numerical Recipes cont 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 problems For example, arrays in C version are handled differently than in C++ version

26. 26 Using Numerical Recipes cont Three different ways to add NR to your project 1. 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

27. 27 Using Numerical Recipes cont Example: Using an NR random number generator Problem: Want standard normal pseudorandom variable Solution: use gasdev() from NR

28. 28 Using Numerical Recipes cont #include #include "nr.h"... // let's generate 100 standard normal variables double normals[100]; // seed the random number generator int idum = -time(NULL); for (int i = 0; i < 100; i++) { normals[i] = NR::gasdev(idum); }...

29. 29 Putting it All Together – A Geometric Brownian Motion Class We want to: Model drift, diffusion Reuse the same object over and over to generate different paths

30. 30 GBM cont 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

31. 31 Code #include #include "nr.h" class CGBMotion { public: // our properties int m_nIdum; // used by NR::gasdev double m_nSInitial; // initial security value (constant) double m_nDrift; // our drift (constant) double m_nSigma; // our volatility (constant) double m_nCurrentTime; // the current elapsed time double m_nCurrentDiffusion; // how much the process has diffused

32. 32 Code cont... public: // our constructor CGBMotion(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; }

33. 33 Code cont... 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 time m_nCurrentDiffusion += sqrt(nDeltaT) * NR::gasdev(m_nIdum); // update our current time m_nCurrentTime = nTime; }

34. 34 Code cont... 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; } };

35. 35 GBM Sample Program int 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; }

36. 36 3 Great Resources Wikipedia: http://www.wikipedia.orghttp://www.wikipedia.org Wilmott: http://www.wilmott.comhttp://www.wilmott.com Google (of course) : http://www.google.com http://www.google.com

37. 37 Questions / Discussion