### Mathematics 16:643:623 Computational Finance

### Schedule

The course is offered during the Spring semester.

- Schedule and Instructor: Please visit the University's schedule of classes for the instructor, time, and room.
**Sample course schedule**

### Course Abstract

The course will start with Monte Carlo (MC) simulation (in particular, simulation of stochastic differential equations, SDEs) followed by finite difference (FD) methods for ODEs and PDEs. Applications include fixed income models (Vasicek and CIR), stochastic volatility models (Heston, Stein and Stein, and Bates) and credit derivatives (credit default swaps (CDS) and basket derivatives). Students implement models using tools such as C++, MATLAB, Python, and Excel-VBA.

### Pre-requisites and Co-requisites

Math 16:643:621 (Mathematical Finance I), Math 16:643:573 (Numerical Analysis I), ECE 16:332:503 (Programming Methodology (C++) for Finance), or equivalent courses. Co-requisites: Math 16:643:622 (Mathematical Finance II).

### Primary Textbooks

There are no required textbooks but useful background texts include:

P. Glasserman (2003): Monte Carlo methods in financial engineering. Springer

J. Hull (2010): Options, futures and other derivatives. Pearson Prentice Hall.

S.E. Shreve (2004): Stochastic calculus for finance II: Continuous-time models. Springer.

### Canvas

All course content – lecture notes, homework assignments and solutions, exam solutions, supplementary articles, and computer programs – are posted on Canvas and available to registered students.

### Grading

Based on homework assignments

### Class Policies

Please see the MSMF common class policies.

### Weekly Lecturing Agenda and Readings

This will be provided on Canvas.

### Library Reserves

All textbooks referenced on this page should be on reserve in the Hill Center Mathematical Sciences Library (1st floor). Please contact the instructor if reserve copies are insufficient or unavailable.

### Additional Textbooks

Class lectures will draw on material from the following texts and current research articles. Please see the Rutgers Mathematical Finance Reference Texts blog for additional textbooks.

- Y. Achdou and O. Pironneau, Computational Methods for Option Pricing (with C++ code), SIAM, 2005
- P. Glasserman,
*Monte Carlo Methods in Financial Engineering*, Springer, 2003 [**Required**] - M. S. Joshi,
*C++ Design Patterns and Derivatives Pricing*(with code), 2nd edition, Wiley, 2008 [**Required**] - P. Wilmott,
*Paul Wilmott on Quantitative Finance*, 2nd edition, 3 volume set, Wiley, 2006

#### Self-contained Introductions to Computational Finance

D. Tavella, *Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance*, Wiley 2002

R. Seydel, *Tools for Computational Finance*, (with pseudocode) 2nd edition, Springer, 2004

#### Derivative Security Pricing

D. Brigo and F. Mercurio, Interest rate models - theory and practice, with smile, inflation, and credit, 2nd edition, Springer, 2006

R. Cont and P. Tankov, Financial Modeling with Jump Processes, Wiley, 2003

E. Haug, The Complete Guide to Option Pricing Formulas (with CD), 2nd edition, McGraw-Hill, 2006

J. Gatheral, *The Volatility Surface: A Practitioner's Guide*, Wiley, 2006

J. C. Hull, *Options, Futures, and Other Derivatives* (with Excel code), 7th edition, Prentice Hall, 2007

A. Kyprianou, W. Schoutens, and P. Wilmott, *Exotic Option Pricing and Advanced Lévy Models*, Wiley 2005

A. Lipton, *Mathematical methods for foreign exchange: a financial engineer's approach*, World Scientific, 2001

P. Wilmott, *Paul Wilmott on Quantitative Finance*, 2nd edition, 3 volume set, Wiley, 2006

#### Elementary Computational Finance (Excel/VBA or MATLAB based)

K. Back, *A Course in Derivative Securities: Introduction to Theory and Computation* (with CD), Springer, 2005

P. Brandimarte, Numerical Methods in Finance: A MATLAB-Based Introduction (with code), Wiley, 2001

L. Clewlow and C. Strickland, Implementing Derivative Models (with pseudocode), Wiley, 1998

M. Jackson and M. Staunton, Advanced modelling in finance using Excel and VBA (with CD), Wiley, 2001

F. Rouah and G. Vainberg, *Option Pricing Models and Volatility using Excel-VBA* (with CD), Wiley, 2007

#### Advanced Computational Finance and Case Studies

C. Albanese and G. Campolieti, *Advanced Derivatives Pricing and Risk Management: Theory, Tools, and Hands-On Programming Applications*, Academic Press, 2005

G. Fusai and A. Roncoroni, *Implementing Models in Quantitative Finance: Methods and Cases* (with MATLAB code), Wiley, 2006

P. Glasserman, *Monte Carlo Methods in Financial Engineering*, Springer, 2003

P. Jäckel, *Monte Carlo Methods in Finance* (with CD), Wiley, 2002

P. Kloeden and E. Platen, *Numerical Solution of Stochastic Differential Equations*, Springer, 2000

J. London, Modeling Derivatives in C++, Wiley, 2004

J. Topper, *Financial Engineering with Finite Elements*, Wiley, 2005

#### Numerical Methods

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, GNU Scientific Library Reference Manual (free Cygwin/Linux C/C++ code and separate CD for Windows C/C++ code), Network Theory, 2006

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, *Numerical Recipes: The Art of Scientific Computing* (separate CD with C++ code), 3rd edition, Cambridge, 2007

#### C++ Programming for Numerical Computing and Finance

S. Dalton, *Financial Applications Using Excel Add-in Development in C/C++* (with CD), 2nd edition, Wiley, 2007

D. J. Duffy, Financial Instrument Pricing Using C++ (with CD), Wiley, 2004

D. J. Duffy, *Finite Difference Methods in Financial Engineering : A Partial Differential Equation Approach* (with CD), Wiley, 2006

D. J. Duffy, Introduction to C++ for Financial Engineers (with CD), Wiley, 2006

J. R. Hubbard, *Schaum's Outline of Programming with C++* (with code), McGraw-Hill, 2000

M. S. Joshi, *C++ Design Patterns and Derivatives Pricing* (with code), 2nd edition, Wiley, 2008

S. Salleh, A. Zomaya, and S. Abu Bakar, Computing for Numerical Methods using Visual C++ (with code), Wiley, 2008

C. Sengupta, *Financial modeling using C++* (with CD), Wiley, 2007

D. Yang, *C++ and Object-Oriented Numeric Programming for Scientists and Engineers* (with code), Springer, 2001

### Software

Please visit the Quantitative Finance Software blog for a guide to platforms, installation guides, and sample code (C++, MATLAB, and Excel-VBA). C++ compilers, Integrated Development Environments (IDEs) and GSL (Gnu Scientific Library) are available for Linux, Cygwin, and Windows.

### External Computational Finance Course Websites

Mark Broadie, Computational Finance, Columbia University website

Bruno Dupire's Computational Finance topic list