# Advanced Finite Difference Method (FDM) for Computational Finance

### Advanced Finite Difference Method (FDM) for Computational Finance

Presented by: Daniel Duffy
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 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.

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

Daniel J. Duffy started the company Datasim in 1987 to promote C++ as a new object-oriented language for developing applications in the roles of developer, architect and requirements analyst to help clients design and analyse software systems for Computer Aided Design (CAD), process control and hardware-software systems, logistics, holography (optical technology) and computational finance. He used a combination of top-down functional decomposition and bottom-up object-oriented programming techniques to create stable and extendible applications (for a discussion, see Duffy 2004 where we have grouped applications into domain categories). Previous to Datasim he worked on engineering applications in oil and gas and semiconductor industries using a range of numerical methods (for example, the finite element method (FEM)) on mainframe and mini-computers.

Daniel Duffy has BA (Mod), MSc and PhD degrees in pure, applied and numerical mathematics from Trinity College, Dublin. He has been active in promoting partial differential equation (PDE) and finite difference methods (FDM) for applications in computational finance and was responsible for the introduction of the Fractional Step (Soviet Splitting) method and the Alternating Direction Explicit (ADE) method in computational finance. He is also the originator of the exponential fitting method for time-dependent partial differential equations.

He is also the originator of two very popular C++ online courses (both C++03 and C++11/14) on www.quantnet.com in cooperation with Quantnet LLC and Baruch College (CUNY), NYC. He also trains developers and designers around the world.

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. Cost: Euro 1500

Duration: 2-4 months

We assume basic knowledge of differential equations and finite difference theory. Familioarity with arithmetical and algebraic manipulation is useful. Knowledge of a mathematical typesetting system (ideally, LaTeX) is strongly recommended.