### Mathematics 16:643:623 Computational Finance

### Schedule

The course is offered during the Spring semester.- Class meeting dates: Please visit the University's academic calendar.
- Schedule and Instructor: Please visit the University's schedule of classes for the instructor, time, and room.
- Instructor and Teaching Assistant Office Hours: Please visit the Mathematical Finance program's office hour schedule.

### Course Abstract

Students learn how to implement financial option-pricing and risk-management models using C++, building on previous and concurrent courses on object-oriented programming with C++, numerical analysis, and mathematical finance. MATLAB, Python, and Excel-VBA may also be used, though primarily as tools for benchmarking and C++ code interfacing. Numerical methods discussed include Monte Carlo simulation, finite difference, finite element, and spectral element solution of partial differential equations, binomial and trinomial trees, the fast Fourier transform (FFT). Asset classes discussed include equities, fixed income and interest rates, foreign exchange, and commodities, though the majority ofapplications will be for equity derivatives for simplicity and access to market data.### 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) and Math 16:643:575 (Numerical Solutions of PDE).### Primary Textbooks

Aside from Glasserman and Joshi, which cover about 40% of the course, there are no other required textbooks, as no single text covers all of the topics. However, we shall cover more of the material in the texts by Glasserman and Joshi than in other single text.- 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

### Sakai

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

Class attendance 5%, homework 15%, two midterm exams at 20% each, and final project 40%. Exams are in-class.### Class Policies

Please see the MSMF common class policies.### Weekly Lecturing Agenda and Readings

This will be provided on Sakai.### 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.#### 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, 2006R. 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, 2006W. 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 websiteBruno Dupire's Computational Finance topic list

Ali Hirsa, Computational Finance, NYU course website