# Distance Learning - Advanced Finite Difference Method (FDM) for Computational Finance

(code DL-FDM)

## DESCRIPTION

The goal of this distance learning course is to approximate the solution of partial differential equations (PDEs) by the Finite Difference Method (FDM) with applications to derivative pricing in computational finance. This course is an in-depth introduction from PDE model specification through efficient and accurate finite difference schemes for a range of one-factor and two-factor option pricing problems. The focus is on understanding the financial, mathematical and numerical skills needed in order to set up the discrete system of equations that we can then implement in C++11, for example.

This course is suitable for front-office and middle-office quant developers who wish to learn the finite difference method for computational finance. The contents of the course is also relevant to other disciplines such as science and engineering.

This course is given in several forms: as distance learning, at client site or as a regular event in various cities.

Subjects Covered

• Specifying financial models as PDEs. Choosing the ‘best’ PDE in a given use case.
• A range of modern finite difference schemes for one and two-factor problems.
• Supporting numerical methods (matrix algebra, nonlinear solvers, interpolators).
• C++11 and library integration.
• Assembling, running and testing the discrete system of equations.

What do you learn?

• The mathematical and numerical foundations of PDE and FDM.
• Applying finite difference methods to computational finance.
• Setting up algorithms and implementing them in a programming language.
• Running, testing and stress-testing the finite difference schemes.

• Do the course at your own pace. No time limit on course access.
• Copies of the books “Finite Difference Methods in Financial Engineering” and “Financial Instrument Pricing using C++, Second Edition” by Daniel J. Duffy.
• Ongoing support via email. Exercises, review and feedback.
• End-of-course exam (e.g. Skype) and Certificate.

We also provide a C++11 software framework (with full source code) that you can use in your work to test your schemes. Of course, you can use other languages such as Python or C#, for example.

Prerequisites

We assume basic knowledge of differential equations and finite difference theory. The models and examples in the course are taken from computational finance.

Some skills in arithmetical and algebraic manipulation are useful, especially when assembling systems of discrete equations.

Knowledge of a mathematical typesetting system (ideally, LaTeX) is strongly recommended.

Who should attend?

This course has been developed so that you can use the theory to solve existing problems as well as applying the knowledge to the pricing of new financial instruments. In particular, the course is for professionals with a strong mathematical background:

• Financial engineers who design new pricing models
• Analysts and quants
• Other professionals who wish to understand and apply advanced numerical methods to derivatives pricing

Trainer and Originator

Daniel J. Duffy is the originator and mentor of this course. He has a PhD in the numerical analysis of partial differential equations from the University of Dublin (Trinity College).

The optimal way to learn in our opinion is by executing the following steps. This discussion pertains to studying and learning the contents of a single module:
1. Listen to the audio show and use the printed PowerPoint slides as printed backup.
2. Read the relevant material in the provided book(s).
3. Do the exercises; compile and run the programs.
4. If you are having problems, go back to one of more of steps 1, 2, 3.
5. If step 4 has been unsuccessful then post your problem on the Datasim forum.
6. Go to next module.

Structure of Course and Student-Trainer Interaction

This course takes an incremental/inductive approach by first examining model problems in detail and then extending them to more advanced applications. Student progress is measured by working on graded exercises. Regular communication takes places by e-mail and Skype.

Students receive a certificate on successful completion of the course.

Course Resources
The course consists of  videos (that you get lifelong access to),  exercises as well as the hard-copies (in pdf format) of the videos.